A280180 -id:A280180 - cp's OEIS frontend

A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 2, 12, 41, 103, 263, 656, 1618, 3931, 9459, 22557, 53395, 125594, 293796, 683972, 1585588, 3661900, 8428646, 19341455, 44261305, 101034472, 230100558, 522936849, 1186138105, 2685582035, 6070360107, 13699764020, 30873005212, 69478759648

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

			Some solutions for n=4:
..0..0. .0..0. .0..0. .0..1. .0..0. .0..1. .0..1. .0..1. .0..1. .0..0
..0..1. .0..0. .0..1. .1..1. .0..0. .0..1. .0..0. .0..0. .0..0. .0..1
..0..1. .0..1. .0..0. .1..1. .1..1. .0..0. .1..0. .0..0. .0..0. .0..1
..0..0. .0..1. .0..1. .0..1. .0..1. .0..0. .0..0. .1..1. .1..0. .1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 2 of A280180.

Empirical: a(n) = 4*a(n-1) - 11*a(n-3) - 4*a(n-4) + 15*a(n-5) + 14*a(n-6) - 2*a(n-7) - 9*a(n-8) - 5*a(n-9) - a(n-10) for n>14.

Empirical g.f.: x*(1 - 2*x + 4*x^2 + 4*x^3 - 35*x^4 - 24*x^5 + 59*x^6 + 85*x^7 - 6*x^8 - 69*x^9 - 43*x^10 - 5*x^11 + 3*x^12 + x^13) / ((1 - x)*(1 - x - 2*x^2 - x^3)^3). - Colin Barker, Feb 13 2019

A280175 Number of nX3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 12, 60, 279, 1082, 3931, 13720, 46467, 153650, 499289, 1598693, 5059881, 15855622, 49273183, 152010000, 466006394, 1420614227, 4309242893, 13013193556, 39139655092, 117289714264, 350310455965, 1043078536630, 3097120192877

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

Column 3 of A280180.

			Some solutions for n=4
..0..0..0. .0..1..1. .0..1..1. .0..0..0. .0..1..1. .0..1..1. .0..1..0
..0..1..0. .1..1..0. .0..1..1. .1..1..0. .1..1..1. .0..1..0. .0..0..0
..1..0..0. .1..1..1. .0..1..0. .1..1..1. .1..0..1. .1..0..0. .0..0..0
..1..1..1. .1..1..1. .1..1..0. .0..1..1. .1..1..1. .0..0..0. .1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A280180.

Empirical: a(n) = 9*a(n-1) -24*a(n-2) -9*a(n-3) +147*a(n-4) -213*a(n-5) -80*a(n-6) +567*a(n-7) -624*a(n-8) -30*a(n-9) +711*a(n-10) -687*a(n-11) +215*a(n-12) +84*a(n-13) +3*a(n-14) -86*a(n-15) +27*a(n-16) +6*a(n-17) -17*a(n-18) -18*a(n-19) -6*a(n-20) -a(n-21) for n>28

A280176 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 41, 279, 1633, 8759, 43094, 202693, 919058, 4057457, 17554353, 74755040, 314269010, 1307053311, 5386675841, 22025521567, 89442385391, 361014889345, 1449314491017, 5790282988659, 23032601187928, 91257530191537

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

Column 4 of A280180.

			Some solutions for n=4
..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..1..1..0
..0..1..1..0. .0..0..0..0. .0..1..1..1. .0..1..1..0. .0..1..0..0
..0..1..1..1. .1..1..0..1. .0..0..0..0. .1..0..1..0. .0..0..0..0
..0..0..1..1. .1..1..0..1. .1..0..0..1. .1..1..1..0. .0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A280180.

Empirical: a(n) = 12*a(n-1) -36*a(n-2) -95*a(n-3) +636*a(n-4) -114*a(n-5) -4112*a(n-6) +3501*a(n-7) +15858*a(n-8) -14979*a(n-9) -50898*a(n-10) +32472*a(n-11) +155801*a(n-12) -45672*a(n-13) -392154*a(n-14) +6334*a(n-15) +749964*a(n-16) +263487*a(n-17) -1160906*a(n-18) -865320*a(n-19) +1407168*a(n-20) +1507520*a(n-21) -1000752*a(n-22) -1913922*a(n-23) +131582*a(n-24) +1715757*a(n-25) +370377*a(n-26) -692041*a(n-27) -487062*a(n-28) -59226*a(n-29) +231552*a(n-30) +194424*a(n-31) -19149*a(n-32) -65094*a(n-33) -26457*a(n-34) -891*a(n-35) +9182*a(n-36) +4908*a(n-37) -726*a(n-38) -746*a(n-39) -222*a(n-40) -24*a(n-41) +60*a(n-42) +12*a(n-43) -9*a(n-44) +a(n-45) for n>54

A280177 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 103, 1082, 8759, 63336, 421214, 2665301, 16203600, 95738359, 553426602, 3144390918, 17616571929, 97552223101, 534893931388, 2908144474219, 15695105501976, 84158923368105, 448686881821760, 2379904102120128

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

Column 5 of A280180.

			Some solutions for n=4
..0..0..1..1..1. .0..0..0..1..1. .0..0..0..1..0. .0..0..0..0..0
..0..1..1..0..1. .1..1..0..1..1. .1..1..1..1..0. .0..1..1..1..0
..0..1..0..0..1. .1..0..1..1..1. .1..1..1..0..0. .1..1..1..0..0
..1..1..0..0..1. .0..0..1..1..1. .1..1..1..0..0. .0..1..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A280180.

A280178 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

9, 263, 3931, 43094, 421214, 3755997, 31821879, 258976696, 2046791216, 15814457993, 120011332264, 897444910233, 6629487497213, 48466584078054, 351182574432103, 2524953934109755, 18030795547257916, 127983331651736137

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

Column 6 of A280180.

			Some solutions for n=4
..0..0..0..1..0..0. .0..1..1..1..1..1. .0..0..1..1..1..1. .0..0..0..0..0..1
..1..1..1..1..0..1. .0..1..1..1..0..0. .0..0..1..0..0..0. .0..0..1..1..1..1
..1..1..1..0..1..1. .0..1..0..0..0..0. .0..0..1..1..0..0. .0..1..1..0..0..1
..0..0..0..0..1..1. .0..0..0..0..0..0. .0..0..1..1..0..0. .1..1..1..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A280180.

A280179 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 656, 13720, 202693, 2665301, 31821879, 359880117, 3910652938, 41205820599, 424186764568, 4286516071132, 42663698232264, 419306557225259, 4077141776062489, 39281413060768999, 375445083262145664

Offset: 1

R. H. Hardin, Dec 28 2016

nonn

Column 7 of A280180.

			Some solutions for n=3
..0..0..0..1..1..0..0. .0..0..0..0..1..1..1. .0..0..0..0..0..1..1
..0..0..1..1..1..0..1. .0..0..0..0..1..1..1. .0..0..1..1..0..1..1
..0..0..0..0..0..1..1. .1..0..0..0..0..0..1. .1..1..1..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A280180.

cp's OEIS Frontend

A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A280175 Number of nX3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A280176 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A280177 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A280178 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A280179 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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