A279466 -id:A279466 - cp's OEIS frontend

A279460 Number of n X 2 0..1 arrays with no element equal 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, 2, 6, 20, 66, 210, 658, 2036, 6236, 18928, 57032, 170790, 508748, 1508462, 4454576, 13107640, 38446722, 112448726, 328044512, 954771282, 2772970950, 8038036642, 23258558892, 67190053760, 193807573324, 558249440024, 1605908314802

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

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

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

Column 2 of A279466.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-4) - 14*a(n-5) - 14*a(n-6) - 14*a(n-7) - 13*a(n-8) - 6*a(n-9) - a(n-10).

Empirical g.f.: 2*x^2*(1 + x)*(1 - 2*x + 2*x^2 - 3*x^3 - x^4 - x^5 - x^6) / (1 - 2*x - x^2 - 2*x^3 - 3*x^4 - x^5)^2. - Colin Barker, Feb 11 2019

A279461 Number of n X 3 0..1 arrays with no element equal 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, 6, 33, 180, 1024, 5228, 26670, 134438, 670407, 3310176, 16219930, 78973826, 382408399, 1842856150, 8843787665, 42284752666, 201514337962, 957534960784, 4537926120718, 21454758254236, 101215638872346, 476553258095432

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

Column 3 of A279466.

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

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

Cf. A279466.

Empirical: a(n) = 10*a(n-1) -33*a(n-2) +58*a(n-3) -110*a(n-4) +76*a(n-5) -37*a(n-6) +46*a(n-7) +216*a(n-8) -90*a(n-9) +274*a(n-10) -480*a(n-11) -570*a(n-12) +82*a(n-13) -243*a(n-14) +666*a(n-15) +1279*a(n-16) +1154*a(n-17) -450*a(n-18) -3012*a(n-19) -1514*a(n-20) +298*a(n-21) -265*a(n-22) +2182*a(n-23) +4582*a(n-24) +864*a(n-25) -4441*a(n-26) -4314*a(n-27) -91*a(n-28) +2472*a(n-29) +1759*a(n-30) +214*a(n-31) -414*a(n-32) -306*a(n-33) -100*a(n-34) -16*a(n-35) -a(n-36).

A279462 Number of nX4 0..1 arrays with no element equal 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, 20, 180, 1722, 15484, 129914, 1079792, 8845592, 71540206, 572555634, 4544198480, 35814522446, 280584310722, 2186897305592, 16968580781888, 131145107324352, 1010053181919720, 7755079215544062, 59376833021426668

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

Column 4 of A279466.

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

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

Cf. A279466.

A279463 Number of nX5 0..1 arrays with no element equal 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, 66, 1024, 15484, 223261, 3086910, 41706415, 555052466, 7290902341, 94741575142, 1220402478079, 15606462944668, 198344727196650, 2507419882264676, 31552047403315039, 395430103470867594

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

Column 5 of A279466.

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

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

Cf. A279466.

A279464 Number of nX6 0..1 arrays with no element equal 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, 210, 5228, 129914, 3086910, 69493918, 1529974962, 33126514762, 707716447612, 14949807134092, 312951296969010, 6502024596897858, 134230949193071182, 2756009011243310442, 56318237615423387758, 1146080901776197182536

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

Column 6 of A279466.

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

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

Cf. A279466.

A279465 Number of nX7 0..1 arrays with no element equal 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, 658, 26670, 1079792, 41706415, 1529974962, 54755104784, 1926654903560, 66854006751350, 2293311539588776, 77940818083281196, 2628632829003297482, 88079138411703964163, 2934932008298081335876, 97326119686256417416192

Offset: 1

R. H. Hardin, Dec 12 2016

nonn

Column 7 of A279466.

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

R. H. Hardin, Table of n, a(n) for n = 1..103

Cf. A279466.

cp's OEIS Frontend

A279460 Number of n X 2 0..1 arrays with no element equal 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

A279461 Number of n X 3 0..1 arrays with no element equal 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

A279462 Number of nX4 0..1 arrays with no element equal 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

A279463 Number of nX5 0..1 arrays with no element equal 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

A279464 Number of nX6 0..1 arrays with no element equal 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

A279465 Number of nX7 0..1 arrays with no element equal 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