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Search: a283950 -id:a283950
Displaying 1-10 of 11 results found. page 1 2
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A283945 Number of nX3 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 2, 87, 900, 8184, 71486, 597042, 4841992, 38481035, 301045074, 2325973337, 17791497852, 134963190603, 1016694067048, 7613544177440, 56723271609684, 420727176381709, 3108419156136654, 22886154154768656, 167982184418042992 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 3 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 14*a(n-1) -53*a(n-2) +66*a(n-3) -370*a(n-4) +772*a(n-5) -629*a(n-6) +2740*a(n-7) -3912*a(n-8) +2424*a(n-9) -8276*a(n-10) +9824*a(n-11) -5152*a(n-12) +8320*a(n-13) -10816*a(n-14) +5632*a(n-15) -1024*a(n-16)
EXAMPLE
Some solutions for n=4
..0..0..0. .1..1..1. .1..1..1. .0..0..0. .1..0..1. .1..1..1. .0..0..0
..1..0..1. .1..0..1. .0..1..1. .1..0..1. .1..0..1. .1..1..0. .1..0..1
..0..1..1. .0..1..0. .1..0..0. .0..1..1. .1..1..1. .0..1..1. .1..1..1
..0..1..1. .0..0..0. .0..0..1. .1..0..0. .0..1..1. .0..0..0. .0..1..0
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283946 Number of nX4 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 16, 906, 16648, 283208, 4510608, 68693470, 1016922620, 14739946302, 210244817456, 2961229080584, 41284559423328, 570755049480396, 7835153742442852, 106914860440688980, 1451387421319840428 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 4 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 22*a(n-1) -79*a(n-2) -404*a(n-3) -1735*a(n-4) +5380*a(n-5) +19741*a(n-6) +34190*a(n-7) -114058*a(n-8) -262182*a(n-9) -147141*a(n-10) +773852*a(n-11) +1033244*a(n-12) -636288*a(n-13) -1952548*a(n-14) -773524*a(n-15) +3381918*a(n-16) +701852*a(n-17) -2086167*a(n-18) -1415394*a(n-19) +277411*a(n-20) +2329064*a(n-21) -1494802*a(n-22) +674022*a(n-23) -1245796*a(n-24) +983860*a(n-25) -532781*a(n-26) +405164*a(n-27) -201292*a(n-28) +71680*a(n-29) -28816*a(n-30) +7280*a(n-31) -1128*a(n-32) +96*a(n-33) -4*a(n-34)
EXAMPLE
Some solutions for n=4
..1..1..1..1. .1..1..0..1. .0..0..0..0. .0..0..0..0. .1..0..1..0
..0..0..1..1. .1..1..1..0. .0..0..0..1. .0..1..0..0. .1..0..0..0
..1..0..0..1. .1..0..0..0. .1..0..1..0. .1..0..1..1. .0..1..1..1
..1..0..1..1. .0..1..1..1. .1..1..1..1. .0..1..0..1. .1..1..0..1
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283947 Number of nX5 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 84, 7988, 264482, 8244557, 242330064, 6816984648, 186634970946, 5006741437429, 132235076658212, 3449881843194282, 89112251221774946, 2282954398345404380, 58083724718538740624, 1469105340510703161357 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 5 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 90
FORMULA
Empirical recurrence of order 90 (see link above)
EXAMPLE
Some solutions for n=3
..0..0..1..0..1. .0..1..1..0..1. .0..1..0..0..1. .1..1..0..0..0
..1..1..0..0..0. .1..1..1..0..1. .0..1..0..1..1. .1..1..0..1..0
..1..0..1..1..1. .1..0..0..1..0. .0..1..1..1..0. .0..1..1..1..1
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283948 Number of nX6 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 408, 69468, 4242700, 241796070, 13010689912, 669777003928, 33569301548620, 1648776677140184, 79729758214875372, 3808601116917731110, 180135397053029043408, 8450230315310614813812, 393679533146957194152168 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 6 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=3
..1..1..1..0..1..0. .1..1..1..1..1..0. .0..1..1..1..1..0. .1..0..0..1..1..0
..1..0..1..0..0..1. .1..0..1..0..0..1. .0..0..1..0..1..1. .1..0..1..0..1..1
..0..0..1..1..1..0. .0..0..1..1..0..0. .0..0..1..0..1..1. .1..1..1..0..1..1
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283949 Number of nX7 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 1926, 575456, 64614384, 6763514843, 667015216686, 62944601744067, 5782000278310300, 520411514987541560, 46113717734650843082, 4036254767838742279228, 349783657626468531519474 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 7 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=2
..0..1..0..0..1..1..1. .0..0..0..0..1..1..1. .0..1..1..1..1..1..1
..0..0..1..1..1..0..1. .0..0..0..0..1..0..1. .0..1..0..1..1..0..0
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283951 Number of 2Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 0, 2, 16, 84, 408, 1926, 8776, 38912, 169456, 727914, 3091712, 13010668, 54334792, 225449486, 930278584, 3820249240, 15622389664, 63649588850, 258473068912, 1046543827972, 4226200851704, 17025631341974, 68440231400232 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 2 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 6*a(n-1) -7*a(n-2) +8*a(n-3) -31*a(n-4) -50*a(n-5) -61*a(n-6) -84*a(n-7) -36*a(n-8).
Empirical g.f.: G.f.: 2*x^3*(1+x)^2/(-1+3*x+x^2+7*x^3+6*x^4)^2 . - R. J. Mathar, Mar 21 2017
EXAMPLE
Some solutions for n=4
..1..1..1..1. .1..0..1..0. .1..1..1..0. .1..1..0..1. .1..0..1..1
..1..0..1..1. .1..1..1..0. .1..0..1..0. .0..1..1..1. .1..1..1..0
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283952 Number of 3Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 0, 87, 906, 7988, 69468, 575456, 4604744, 36137513, 279163040, 2128757750, 16067783050, 120264121036, 893798288058, 6602798852295, 48525145143750, 355015663432086, 2587074206224930, 18786624241231104, 135997998678920894 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 3 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 10*a(n-1) -15*a(n-2) +50*a(n-3) -483*a(n-4) -688*a(n-5) -2954*a(n-6) -1998*a(n-7) +1187*a(n-8) +9770*a(n-9) +26575*a(n-10) +21254*a(n-11) -469*a(n-12) -42264*a(n-13) -80523*a(n-14) -54448*a(n-15) +18704*a(n-16) +71312*a(n-17) +57531*a(n-18) +12848*a(n-19) -15198*a(n-20) -17226*a(n-21) -8382*a(n-22) -2048*a(n-23) +107*a(n-24) +234*a(n-25) +59*a(n-26) +4*a(n-27) -4*a(n-28)
EXAMPLE
Some solutions for n=4
..1..1..1..0. .1..1..1..0. .1..1..0..0. .1..0..1..0. .1..0..1..1
..1..1..0..1. .1..1..0..0. .0..0..1..1. .0..1..1..1. .0..1..0..1
..1..0..1..0. .1..1..1..1. .1..1..1..1. .1..0..1..0. .1..0..1..0
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283953 Number of 4Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 0, 900, 16648, 264482, 4242700, 64614384, 948567440, 13692510028, 194684984664, 2732350150328, 37970482883588, 523376223847790, 7164059469775432, 97485442889266544, 1319817637818838080 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 4 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 16*a(n-1) -8*a(n-2) +284*a(n-3) -5868*a(n-4) -28230*a(n-5) -157554*a(n-6) -173236*a(n-7) +1146756*a(n-8) +7892098*a(n-9) +25593935*a(n-10) +36554864*a(n-11) -55986547*a(n-12) -432158954*a(n-13) -1204632264*a(n-14) -1998691250*a(n-15) -1605250954*a(n-16) +294441830*a(n-17) +809141749*a(n-18) -1344109538*a(n-19) -103523380*a(n-20) +5289951936*a(n-21) +2914513239*a(n-22) -5852825596*a(n-23) -3883862757*a(n-24) +6008029086*a(n-25) +3960433969*a(n-26) -6028634000*a(n-27) -2764777189*a(n-28) +6310228182*a(n-29) +2948307946*a(n-30) -4841207198*a(n-31) -3654980824*a(n-32) +1938808856*a(n-33) +2350470949*a(n-34) -14404886*a(n-35) -836811271*a(n-36) -578351728*a(n-37) +95766913*a(n-38) +329294420*a(n-39) +51047632*a(n-40) -103322336*a(n-41) +3540417*a(n-42) +53070582*a(n-43) +4003494*a(n-44) -9177612*a(n-45) -7358386*a(n-46) -3173056*a(n-47) +1093461*a(n-48) +565312*a(n-49) -841952*a(n-50) -282366*a(n-51) +325420*a(n-52) +31324*a(n-53) -41337*a(n-54) +5404*a(n-55) -196*a(n-56)
EXAMPLE
Some solutions for n=4
..0..0..0..1. .1..0..0..0. .0..0..1..1. .1..0..1..0. .1..1..0..0
..1..1..1..1. .1..0..1..0. .1..1..1..1. .1..0..0..0. .0..0..0..0
..0..1..0..1. .1..1..1..0. .0..0..0..1. .1..0..1..1. .1..0..1..0
..1..1..0..0. .0..1..0..1. .0..0..1..1. .1..1..1..0. .1..1..1..1
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283954 Number of 5Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 0, 8184, 283208, 8244557, 241796070, 6763514843, 182198176994, 4825164796310, 125933665031272, 3244468947083396, 82767450195612832, 2094459557648313968, 52635795570355253222, 1315036944531836311688, 32688961006164835305772 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 5 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=3
..1..0..1. .1..0..1. .1..1..1. .1..1..1. .1..1..1. .1..1..0. .1..0..1
..1..1..0. .1..1..1. .0..0..1. .0..0..1. .0..0..0. .0..0..0. .1..0..0
..0..1..1. .0..1..0. .1..0..1. .1..1..0. .1..1..1. .1..1..1. .0..0..1
..1..0..0. .0..1..1. .0..1..1. .1..0..1. .1..1..0. .1..1..0. .0..1..1
..0..1..0. .1..0..0. .1..1..0. .1..0..1. .0..1..1. .1..1..1. .1..0..1
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
A283955 Number of 6Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. +10
1
0, 0, 71486, 4510608, 242330064, 13010689912, 667015216686, 32960788748780, 1600697201681958, 76611709398415200, 3619757534989162198, 169346455636754049580, 7859113340842715699470, 362219493645285494837272 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row 6 of A283950.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=3
..1..1..1. .1..1..0. .1..0..0. .1..1..1. .1..1..0. .0..0..1. .0..0..1
..0..1..1. .1..0..1. .0..0..0. .1..1..0. .1..0..1. .0..0..1. .0..0..1
..1..0..1. .1..1..1. .0..1..1. .0..0..1. .1..1..0. .0..1..1. .1..1..1
..0..0..1. .1..1..0. .1..1..1. .1..0..0. .0..0..1. .0..0..1. .0..1..1
..1..0..0. .0..0..0. .1..0..0. .1..1..1. .1..0..0. .1..0..1. .0..0..0
..0..0..1. .1..0..1. .1..0..0. .0..0..0. .1..0..0. .1..1..1. .1..1..0
CROSSREFS
Cf. A283950.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2017
STATUS
approved
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Last modified August 29 18:55 EDT 2024. Contains 375518 sequences. (Running on oeis4.)