A241130 -id:A241130 - cp's OEIS frontend

A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

2, 9, 54, 325, 1965, 11876, 71793, 434007, 2623694, 15861001, 95884409, 579649484, 3504151829, 21183629803, 128061281038, 774168159805, 4680074530261, 28292428888436, 171036065180937, 1033963386740399, 6250613190784174

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

			Some solutions for n=4:
..0..1....0..1....0..0....0..1....0..1....0..1....0..1....0..1....0..0....0..1
..1..2....0..1....1..2....2..0....0..2....1..0....1..0....1..2....1..2....0..1
..2..0....1..2....0..1....0..1....1..1....0..1....1..2....1..0....0..2....1..0
..1..1....2..0....1..2....0..1....2..2....0..2....2..0....0..1....0..1....1..0

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

Column 2 of A241130.

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

Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 + 3*x + x^2 - 2*x^3) / (1 - 6*x - 2*x^2 + 9*x^3 + 10*x^4 - 8*x^5). - Colin Barker, Oct 29 2018

A241126 Number of nX3 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

4, 54, 723, 9773, 132369, 1792237, 24269723, 328645291, 4450319537, 60263615333, 816054461063, 11050530322615, 149639792084929, 2026334190350265, 27439427668181531, 371568616043522567, 5031563999805819365

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 3 of A241130

			Some solutions for n=4
..0..1..1....0..1..1....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
..1..0..0....2..0..2....2..0..1....1..0..2....0..2..1....0..2..1....1..2..0
..0..2..1....1..0..2....1..0..1....0..1..0....1..0..2....1..2..1....0..1..1
..1..2..0....2..1..1....2..1..0....2..1..2....2..0..1....0..1..2....1..2..0

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

Empirical: a(n) = 14*a(n-1) -7*a(n-2) +27*a(n-3) -170*a(n-4) -631*a(n-5) -1135*a(n-6) +5278*a(n-7) -3113*a(n-8) +5125*a(n-9) +13678*a(n-10) -10325*a(n-11) +15744*a(n-12) -52520*a(n-13) -13756*a(n-14) -110176*a(n-15) +64424*a(n-16) -53672*a(n-17) -13552*a(n-18) +87456*a(n-19) -198528*a(n-20) +71552*a(n-21) -44288*a(n-22) -116224*a(n-23) -4096*a(n-24) -122880*a(n-25) -65536*a(n-26)

A241127 Number of nX4 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

11, 325, 9773, 295584, 8974020, 272418756, 8270609664, 251096788713, 7623351508315, 231446775293031, 7026779711400192, 213334731852107120, 6476894113062087316, 196640073775126182008, 5970040263453594766199

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 4 of A241130

			Some solutions for n=3
..0..1..2..0....0..1..2..0....0..1..0..1....0..0..1..0....0..0..0..1
..2..1..2..0....2..1..0..2....2..1..1..2....1..1..2..1....2..0..2..0
..1..2..0..1....0..2..2..1....0..1..0..1....2..0..0..2....0..2..1..1

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

A241128 Number of nX5 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

30, 1965, 132369, 8974020, 611547441, 41661463219, 2838552905280, 193403197619803, 13177423185201303, 897837461485635262, 61173728850055840649, 4168043075184317942781, 283987643903962340437622

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 5 of A241130

			Some solutions for n=3
..0..1..2..0..1....0..0..1..2..0....0..1..0..1..0....0..1..2..1..1
..2..1..0..2..2....2..1..0..1..2....2..2..0..0..2....1..0..2..0..0
..0..2..2..1..0....0..1..2..1..0....1..1..0..1..0....0..0..0..2..2

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

A241129 Number of nX6 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

82, 11876, 1792237, 272418756, 41661463219, 6369134821236, 973866422990563, 148910067386335603, 22769250775360645781, 3481561098182183872590, 532352524971939702558325, 81400042312275755768027497

Offset: 1

R. H. Hardin, Apr 16 2014

nonn

Column 6 of A241130

			Some solutions for n=2
..0..1..1..1..2..1....0..1..0..2..0..2....0..1..0..1..0..1....0..1..2..1..2..1
..0..2..1..0..1..0....1..0..2..0..0..0....1..0..0..0..1..2....2..2..0..0..2..0

R. H. Hardin, Table of n, a(n) for n = 1..57

cp's OEIS Frontend

A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

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A241126 Number of nX3 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

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A241127 Number of nX4 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

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A241128 Number of nX5 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

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A241129 Number of nX6 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

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