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Search: a298133 -id:a298133
Displaying 1-6 of 6 results found.
page 1
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A298128
Number of nX3 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
1
0, 2, 4, 13, 62, 223, 826, 3200, 12098, 45921, 174562, 662609, 2516820, 9558976, 36301634, 137870761, 523613086, 1988599181, 7552421216, 28682975530, 108933718764, 413714339533, 1571226249932, 5967286725891, 22662879439242
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 3 of A298133.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) +4*a(n-2) -12*a(n-4) -7*a(n-5) -2*a(n-6) -13*a(n-7) +46*a(n-8) +28*a(n-9) -78*a(n-10) -23*a(n-11) +61*a(n-12) +14*a(n-13) -8*a(n-14) -2*a(n-15) -14*a(n-16) +4*a(n-18)
EXAMPLE
Some solutions for n=7
..0..1..1. .0..1..1. .0..0..1. .0..0..1. .0..0..0. .0..0..1. .0..0..1
..0..0..1. .0..0..1. .0..1..1. .0..1..1. .1..0..1. .0..1..1. .0..1..1
..0..0..1. .1..1..0. .0..1..0. .1..0..0. .1..1..1. .0..1..0. .1..0..1
..0..1..1. .1..0..0. .0..0..0. .1..1..0. .1..1..1. .1..0..0. .1..0..0
..0..1..1. .0..1..1. .1..1..1. .1..1..0. .1..0..1. .1..1..1. .0..1..1
..0..1..0. .0..1..1. .0..1..0. .0..1..0. .1..0..0. .0..0..1. .0..1..0
..0..0..0. .0..0..1. .0..0..0. .0..0..0. .1..1..0. .0..1..1. .0..0..0
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
A298129
Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
1
0, 5, 13, 15, 233, 1055, 5782, 36225, 205348, 1209336, 7104221, 41593299, 244217670, 1432727023, 8406086075, 49326923443, 289428447489, 1698283766510, 9965061067996, 58472010523076, 343097200672431, 2013196295930588
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 4 of A298133.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) +18*a(n-2) +25*a(n-3) -115*a(n-4) -418*a(n-5) -362*a(n-6) +1223*a(n-7) +4240*a(n-8) +2290*a(n-9) -9359*a(n-10) -16112*a(n-11) +3825*a(n-12) +30881*a(n-13) +10497*a(n-14) -37030*a(n-15) -21624*a(n-16) +40949*a(n-17) +30128*a(n-18) -52580*a(n-19) -29839*a(n-20) +16613*a(n-21) -97187*a(n-22) -8185*a(n-23) +199948*a(n-24) +235970*a(n-25) +21467*a(n-26) -396028*a(n-27) -168777*a(n-28) +347284*a(n-29) +546093*a(n-30) -20595*a(n-31) -733067*a(n-32) -497232*a(n-33) +64780*a(n-34) +471056*a(n-35) +244089*a(n-36) -113651*a(n-37) -210162*a(n-38) -106774*a(n-39) +42085*a(n-40) -11265*a(n-41) -9272*a(n-42) +5459*a(n-43) +12341*a(n-44) +24615*a(n-45) +7030*a(n-46) -4538*a(n-47) -4658*a(n-48) -2118*a(n-49) +128*a(n-50) +580*a(n-51) -4*a(n-52) -40*a(n-53) for n>56
EXAMPLE
Some solutions for n=7
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .0..1..0..1
..0..0..1..0. .1..1..0..0. .1..1..1..0. .1..0..1..0. .1..0..0..0
..1..1..0..1. .0..1..1..0. .1..0..0..1. .1..0..1..0. .0..1..1..0
..1..0..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..0. .1..0..0..1
..1..0..0..1. .1..0..1..0. .0..1..1..0. .0..1..0..1. .1..0..1..0
..1..1..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
A298130
Number of nX5 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
1
0, 10, 62, 233, 2621, 21537, 175014, 1557284, 13225388, 115057043, 995377715, 8609735775, 74634586211, 646239250543, 5597827267858, 48490327697080, 420018142359036, 3638291956178446, 31515344567810130, 272991120320041375
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 5 of A298133.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=7
..0..0..0..0..1. .0..0..0..1..1. .0..0..0..0..0. .0..0..1..1..1
..0..1..0..1..1. .0..1..0..1..1. .0..1..0..1..0. .0..1..0..0..1
..0..1..1..0..1. .1..0..1..0..0. .1..1..0..1..1. .1..1..0..1..1
..0..0..0..1..1. .0..1..0..1..0. .1..0..0..1..0. .1..0..1..0..0
..1..1..1..0..0. .0..1..0..1..1. .1..0..1..0..0. .0..1..0..1..0
..0..1..0..1..0. .0..1..0..1..0. .0..1..1..0..1. .1..0..1..1..0
..0..0..1..0..0. .0..0..1..0..0. .0..0..1..1..1. .1..1..0..0..0
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
A298131
Number of nX6 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
1
0, 25, 223, 1055, 21537, 285084, 3752401, 52922003, 714854991, 9882443650, 135778074542, 1864072607185, 25646093419747, 352488786489609, 4845708865503389, 66618364620496743, 915822218872378347
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 6 of A298133.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=5
..0..0..1..0..0..0. .0..0..1..1..0..0. .0..0..1..1..0..0. .0..0..0..1..1..1
..0..1..0..1..1..0. .0..1..0..1..1..0. .0..1..0..0..1..0. .0..1..1..0..0..1
..0..1..1..0..1..0. .0..1..0..0..1..1. .0..0..1..1..0..0. .1..1..0..1..0..1
..0..0..1..0..0..1. .1..0..1..0..1..0. .1..1..0..1..0..1. .0..1..0..1..0..1
..0..1..1..0..1..1. .1..1..0..1..0..0. .1..1..0..0..1..1. .0..0..0..0..1..1
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
A298132
Number of nX7 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
1
0, 54, 826, 5782, 175014, 3752401, 76791444, 1706951987, 36185741209, 786733395586, 16992126182076, 366550521559787, 7927928295359425, 171260155001322160, 3700464812129655258, 79963026370989545009
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 7 of A298133.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=5
..0..0..1..0..1..1..1. .0..0..1..1..0..0..0. .0..0..1..0..0..0..0
..0..1..0..1..0..1..1. .0..1..1..1..1..0..1. .0..1..0..1..1..1..0
..0..0..1..1..0..0..0. .0..0..0..0..0..1..1. .0..0..1..0..0..0..1
..1..0..1..0..1..0..1. .0..1..1..0..0..1..0. .1..0..1..1..1..0..1
..1..1..1..0..0..1..1. .1..1..1..1..1..0..0. .1..1..0..0..0..1..1
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
A298127
Number of n X n 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
+10
0
0, 1, 4, 15, 2621, 285084, 76791444, 58599163176, 99650656591710, 437509891251025898
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Diagonal of A298133.
LINKS
Table of n, a(n) for n=1..10.
EXAMPLE
Some solutions for n=5
..0..0..1..1..1. .0..0..1..1..0. .0..0..0..1..1. .0..0..1..1..1
..0..1..0..0..1. .1..0..1..0..0. .0..1..0..0..1. .0..0..1..0..1
..1..0..0..1..0. .1..1..0..1..0. .1..0..1..1..1. .1..1..0..0..0
..0..1..1..0..1. .1..0..0..1..0. .0..1..1..0..0. .1..0..1..1..0
..0..0..1..1..1. .1..1..1..0..0. .0..0..1..0..0. .0..0..1..1..1
CROSSREFS
Cf. A298133.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 13 2018
STATUS
approved
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