A279972 Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 9, 50, 296, 1650, 8666, 43543, 211650, 1002602, 4652327, 21225237, 95473540, 424318824, 1866436977, 8136431834, 35191126234, 151149336828, 645183934470, 2738696392197, 11567109056460, 48632928912442, 203627897130121

Offset

1,2

Links

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

Formula

Empirical: a(n) = 15*a(n-1) - 90*a(n-2) + 281*a(n-3) - 510*a(n-4) + 585*a(n-5) - 437*a(n-6) + 210*a(n-7) - 60*a(n-8) + 8*a(n-9) for n>10.

Empirical g.f.: x^2*(9 - 85*x + 356*x^2 - 819*x^3 + 1096*x^4 - 888*x^5 + 438*x^6 - 124*x^7 + 16*x^8) / (1 - 5*x + 5*x^2 - 2*x^3)^3. - Colin Barker, Feb 12 2019

Example

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

Crossrefs

Column 3 of A279977.

Sequence in context: A341921 A231413 A007681 * A115366 A188210 A308646

Adjacent sequences: A279969 A279970 A279971 * A279973 A279974 A279975

Keyword

nonn

Author

R. H. Hardin, Dec 24 2016

Status

approved