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Search: a223999 -id:a223999
Displaying 1-10 of 12 results found. page 1 2
     Sort: relevance | references | number | modified | created      Format: long | short | data
A223994 Number of nX3 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
10, 76, 476, 2980, 18672, 117386, 739672, 4664776, 29428242, 185670484, 1171477424, 7391425016, 46636189140, 294251036912, 1856576835280, 11714070469768, 73909919072136, 466334575535548, 2942337620960936 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 10*a(n-1) -24*a(n-2) -2*a(n-3) +30*a(n-4) +96*a(n-5) -150*a(n-6) -108*a(n-7) +48*a(n-8) +270*a(n-9)
EXAMPLE
Some solutions for n=3
..2..2..2....1..1..2....0..0..0....0..0..2....0..1..1....0..0..0....0..1..1
..2..2..2....1..1..2....0..0..2....1..2..2....1..2..2....0..0..1....0..0..2
..0..2..2....0..2..2....1..1..2....0..1..2....1..2..2....1..1..2....0..0..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A223995 Number of nX4 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
15, 155, 1144, 7927, 55333, 388598, 2743444, 19437479, 138010718, 981047716, 6977843175, 49645292212, 353262192994, 2513898151334, 17890175634324, 127318180862693, 906089796193803, 6448444001034017, 45892351529878911 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 15*a(n-1) -69*a(n-2) +66*a(n-3) +226*a(n-4) -172*a(n-5) -1192*a(n-6) +2157*a(n-7) -1714*a(n-8) -2876*a(n-9) +4966*a(n-10) +12095*a(n-11) -17584*a(n-12) +28968*a(n-13) +156*a(n-14) -2874*a(n-15) -2964*a(n-16) +15876*a(n-17) +1008*a(n-18) for n>19
EXAMPLE
Some solutions for n=3
..0..0..2..2....0..1..1..1....0..0..0..0....0..0..1..1....0..1..1..2
..0..1..1..2....1..1..1..2....0..0..2..2....0..0..2..2....0..0..1..2
..1..1..1..1....0..2..2..2....1..1..1..2....0..2..2..2....0..0..1..1
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A223996 Number of nX5 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
21, 281, 2403, 17929, 132119, 984595, 7400832, 55978489, 425257387, 3240026429, 24732295031, 189012200658, 1445524081573, 11059812977060, 84641528773971, 647871404690124, 4959498660501284, 37967742496830194, 290676685330836460 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 21*a(n-1) -155*a(n-2) +405*a(n-3) +365*a(n-4) -2996*a(n-5) -664*a(n-6) +18276*a(n-7) -22433*a(n-8) -2304*a(n-9) -9369*a(n-10) -7644*a(n-11) +222262*a(n-12) +167540*a(n-13) -1508772*a(n-14) +2046821*a(n-15) -1097976*a(n-16) +4265706*a(n-17) -2582500*a(n-18) -941886*a(n-19) -2423080*a(n-20) +19902336*a(n-21) +2548764*a(n-22) +9439760*a(n-23) +1688032*a(n-24) +1035840*a(n-25) -957120*a(n-26) +1996416*a(n-27) -115200*a(n-28) for n>31
EXAMPLE
Some solutions for n=3
..0..0..0..0..0....0..1..1..1..1....0..0..0..0..0....1..1..1..1..2
..0..0..0..2..2....1..1..1..1..1....0..1..1..1..2....0..2..2..2..2
..1..1..1..1..2....0..1..1..2..2....0..2..2..2..2....2..2..2..2..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A223997 Number of nX6 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
28, 469, 4614, 36845, 281271, 2160036, 16795265, 131782267, 1040869367, 8260503068, 65781844983, 525128814213, 4199218263977, 33618978354499, 269371779362318, 2159531269883408, 17319319103903054, 138936031415524052 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 28*a(n-1) -300*a(n-2) +1417*a(n-3) -1482*a(n-4) -11436*a(n-5) +31851*a(n-6) +52359*a(n-7) -290782*a(n-8) +153075*a(n-9) +602260*a(n-10) -176604*a(n-11) -1863678*a(n-12) +536713*a(n-13) +8514601*a(n-14) -7251292*a(n-15) -64571700*a(n-16) +163992784*a(n-17) -63488599*a(n-18) +75157211*a(n-19) -574679221*a(n-20) +1117201234*a(n-21) -1103109981*a(n-22) +247796355*a(n-23) -1415805562*a(n-24) +12828520548*a(n-25) -5049431870*a(n-26) +5717879992*a(n-27) +7921013636*a(n-28) +14497424532*a(n-29) -1161322200*a(n-30) +7782865280*a(n-31) +2703305984*a(n-32) +21857003968*a(n-33) +1446146688*a(n-34) +6372675072*a(n-35) -1634756608*a(n-36) +2474711040*a(n-37) -114278400*a(n-38) +967065600*a(n-39) for n>44
EXAMPLE
Some solutions for n=3
..0..0..0..1..2..2....0..0..1..1..2..2....0..0..0..0..0..0....0..0..0..1..1..1
..2..2..2..2..2..2....0..1..1..2..2..2....0..1..1..2..2..2....0..0..0..1..1..2
..0..2..2..2..2..2....0..1..1..1..2..2....1..2..2..2..2..2....0..0..0..1..1..1
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A223998 Number of nX7 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
36, 736, 8291, 71061, 559188, 4368458, 34534687, 276286000, 2229871293, 18115082917, 147889219961, 1211856739505, 9958518859510, 82010005661441, 676451232895869, 5586333937854878, 46174727441274521, 381916881456838766 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 7 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 54
FORMULA
Empirical recurrence of order 54 (see link above)
EXAMPLE
Some solutions for n=3
..0..0..0..0..0..1..1....0..1..1..1..1..1..1....0..0..0..0..1..1..1
..0..0..0..0..1..1..2....0..0..1..1..1..1..2....0..1..1..1..1..2..2
..1..1..1..2..2..2..2....0..0..1..1..1..2..2....0..0..1..1..1..1..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A224000 Number of 2 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing. +10
1
9, 31, 76, 155, 281, 469, 736, 1101, 1585, 2211, 3004, 3991, 5201, 6665, 8416, 10489, 12921, 15751, 19020, 22771, 27049, 31901, 37376, 43525, 50401, 58059, 66556, 75951, 86305, 97681, 110144, 123761, 138601, 154735, 172236, 191179, 211641, 233701 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 2 of A223999.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = (1/12)*n^4 + 1*n^3 + (41/12)*n^2 + (7/2)*n + 1.
Conjectures from Colin Barker, Aug 25 2018: (Start)
G.f.: x*(9 - 14*x + 11*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..2....0..0..1....1..1..1....0..1..1....1..1..1....0..0..2....1..1..2
..0..0..2....2..2..2....0..1..2....0..1..2....0..1..1....2..2..2....0..2..2
CROSSREFS
Cf. A223999.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2013
STATUS
approved
A224001 Number of 3 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing. +10
1
27, 157, 476, 1144, 2403, 4614, 8291, 14141, 23109, 36428, 55674, 82826, 120331, 171174, 238953, 327959, 443261, 590796, 777464, 1011228, 1301219, 1657846, 2092911, 2619729, 3253253, 4010204, 4909206, 5970926, 7218219, 8676278 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 3 of A223999.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = (1/144)*n^6 + (5/48)*n^5 + (163/144)*n^4 + (85/16)*n^3 + (895/36)*n^2 - (65/12)*n + 3 for n>2.
Conjectures from Colin Barker, Aug 25 2018: (Start)
G.f.: x*(27 - 32*x - 56*x^2 + 164*x^3 - 159*x^4 + 85*x^5 - 32*x^6 + 9*x^7 - x^8) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.
(End)
EXAMPLE
Some solutions for n=3:
..1..2..2....0..1..2....0..1..1....1..2..2....0..0..0....0..0..2....2..2..2
..0..1..2....1..2..2....0..1..2....1..1..2....0..1..2....0..0..0....2..2..2
..1..1..1....2..2..2....0..1..1....1..1..1....0..1..1....0..1..2....1..2..2
CROSSREFS
Cf. A223999.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2013
STATUS
approved
A224002 Number of 4 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing. +10
1
81, 793, 2980, 7927, 17929, 36845, 71061, 130767, 231730, 397675, 663404, 1078800, 1713877, 2665051, 4062821, 6081063, 8948154, 12960157, 18496312, 26037092, 36185097, 49689073, 67471357, 90659063, 120619338, 158999031, 207769132 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 4 of A223999.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = (1/2880)*n^8 + (1/180)*n^7 + (25/288)*n^6 + (169/180)*n^5 + (18649/2880)*n^4 + (4247/90)*n^3 + (2719/16)*n^2 - (6649/30)*n - 17 for n>4.
Conjectures from Colin Barker, Aug 25 2018: (Start)
G.f.: x*(81 + 64*x - 1241*x^2 + 2851*x^3 - 2540*x^4 + 248*x^5 + 1398*x^6 - 1380*x^7 + 796*x^8 - 347*x^9 + 88*x^10 - x^11 - 3*x^12) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..1....1..1..1....0..0..1....0..1..1....0..1..2....1..1..1....0..1..1
..0..2..2....1..1..1....0..1..1....1..1..1....0..1..1....1..1..2....1..1..1
..1..1..2....0..1..2....0..0..1....1..2..2....0..0..2....0..2..2....0..1..1
..1..2..2....0..0..1....0..0..0....0..2..2....0..0..1....2..2..2....0..0..1
CROSSREFS
Cf. A223999.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2013
STATUS
approved
A224003 Number of 5Xn 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
243, 4004, 18672, 55333, 132119, 281271, 559188, 1063365, 1958634, 3517866, 6183395, 10657414, 18032067, 29972868, 48972482, 78695853, 124442202, 193754586, 297213549, 449457950, 670483363, 987276552, 1435853472, 2063778077 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 5 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = (1/86400)*n^10 + (1/5760)*n^9 + (13/3360)*n^8 + (1079/20160)*n^7 + (19031/28800)*n^6 + (35137/5760)*n^5 + (513623/8640)*n^4 + (161053/480)*n^3 + (3838487/2800)*n^2 - (614813/210)*n - 2235 for n>6
EXAMPLE
Some solutions for n=3
..0..2..2....0..0..0....0..0..2....1..1..1....0..2..2....0..0..0....0..0..0
..0..1..2....0..0..1....0..0..0....1..1..1....0..0..2....0..0..2....1..1..2
..0..1..2....0..0..2....0..0..0....1..1..2....0..1..2....1..1..2....0..1..2
..0..1..1....0..2..2....0..1..2....0..2..2....0..0..1....0..1..2....0..0..1
..1..1..2....0..2..2....1..1..1....2..2..2....0..2..2....0..1..1....0..2..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
A224004 Number of 6Xn 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing +10
1
729, 20216, 117386, 388598, 984595, 2160036, 4368458, 8412641, 15703623, 28693082, 51589943, 91524689, 160402902, 277798382, 475383309, 803588211, 1341439640, 2210851797, 3597065144, 5777447600, 9161521721, 14345876103 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 6 of A223999
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = (1/3628800)*n^12 + (1/302400)*n^11 + (419/3628800)*n^10 + (223/120960)*n^9 + (35411/1209600)*n^8 + (20443/50400)*n^7 + (17616857/3628800)*n^6 + (6342323/120960)*n^5 + (821276033/1814400)*n^4 + (103253527/37800)*n^3 + (186412339/16800)*n^2 - (24901729/840)*n - 64275 for n>8
EXAMPLE
Some solutions for n=3
..0..1..1....0..0..0....0..0..0....0..0..2....0..0..0....0..0..0....0..0..2
..0..1..2....0..0..2....0..2..2....1..1..2....0..2..2....0..0..0....0..1..1
..0..0..1....0..0..0....0..1..2....1..1..2....1..2..2....0..0..1....1..1..1
..0..2..2....0..0..0....1..1..1....0..1..1....0..1..2....1..1..2....0..2..2
..1..1..2....0..0..2....0..1..1....0..1..2....0..1..1....1..1..1....1..1..2
..1..1..2....1..1..2....2..2..2....1..2..2....0..2..2....0..1..2....0..1..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved
page 1 2

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Last modified August 29 08:01 EDT 2024. Contains 375510 sequences. (Running on oeis4.)