A280161 -id:A280161 - cp's OEIS frontend

A280155 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 one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 8, 18, 40, 92, 208, 470, 1060, 2384, 5352, 11992, 26824, 59906, 133592, 297510, 661720, 1470062, 3262264, 7231940, 16016596, 35439722, 78349800, 173074816, 382029988, 842648168, 1857362384, 4091321478, 9006604780, 19815365450

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

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

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

Column 2 of A280161.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n>8.

Empirical g.f.: 2*x^2*(2 - 5*x^2 - 6*x^3 - x^4 + 2*x^5 + x^6) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Feb 13 2019

A280156 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 one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 8, 31, 94, 305, 950, 2901, 8728, 26068, 77326, 228367, 671446, 1967328, 5745190, 16730555, 48594066, 140815777, 407186706, 1175159395, 3385527188, 9737463217, 27964574958, 80197812317, 229694924100, 657073271390, 1877519404364

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

Column 3 of A280161.

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

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

Cf. A280161.

Empirical: a(n) = 6*a(n-1) -7*a(n-2) -18*a(n-3) +45*a(n-4) -22*a(n-5) -38*a(n-6) +74*a(n-7) -39*a(n-8) -2*a(n-9) +4*a(n-10) +2*a(n-11) -8*a(n-12) -4*a(n-13) -a(n-14) for n>19

A280157 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 one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 18, 94, 424, 1854, 7628, 30874, 123312, 488256, 1920790, 7513678, 29249892, 113386708, 437908264, 1685639238, 6469357240, 24762845248, 94557090250, 360277506538, 1369975634630, 5199885300498, 19703519987286, 74545164231536

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

Column 4 of A280161.

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

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

Cf. A280161.

Empirical: a(n) = 8*a(n-1) -8*a(n-2) -74*a(n-3) +144*a(n-4) +268*a(n-5) -631*a(n-6) -714*a(n-7) +1344*a(n-8) +2362*a(n-9) -2134*a(n-10) -6068*a(n-11) +2745*a(n-12) +9240*a(n-13) +321*a(n-14) -10644*a(n-15) -5878*a(n-16) +9474*a(n-17) +4820*a(n-18) -1796*a(n-19) -2276*a(n-20) -1436*a(n-21) +58*a(n-22) +800*a(n-23) +187*a(n-24) -46*a(n-25) -43*a(n-26) -28*a(n-27) +a(n-28) +6*a(n-29) -a(n-30) for n>36

A280158 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 one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 40, 305, 1854, 10677, 58852, 318220, 1695030, 8941285, 46760710, 242970442, 1255597078, 6458360287, 33085037590, 168885713050, 859370947890, 4360537440625, 22069557056618, 111441207638795, 561547964534696

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

Column 5 of A280161.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 70

Cf. A280161.

Empirical recurrence of order 70 (see link above)

A280159 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 one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 92, 950, 7628, 58852, 434790, 3138340, 22348406, 157294986, 1097158250, 7598014364, 52296147282, 358119530526, 2441393217986, 16579221466148, 112199621622362, 756987753165838, 5093205986747148, 34183505883347834

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

Column 6 of A280161.

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

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

Cf. A280161.

A280160 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 one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 208, 2901, 30874, 318220, 3138340, 30089398, 285461736, 2671391625, 24767920958, 227975959120, 2085061428192, 18968539604655, 171769706597400, 1549174969429286, 13922125649869206, 124717748809003344

Offset: 1

R. H. Hardin, Dec 27 2016

nonn

Column 7 of A280161.

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

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

Cf. A280161.

cp's OEIS Frontend

A280155 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A280156 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280157 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280158 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A280159 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A280160 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 one element, and with new values introduced in order 0 sequentially upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs