A281402 Number of 3 X n 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 6, 131, 314, 689, 1294, 2364, 4338, 7850, 14150, 25510, 45790, 81958, 146454, 261006, 464062, 823590, 1458790, 2579102, 4552526, 8023638, 14120758, 24818318, 43566366, 76387782, 133790726, 234092798, 409199086, 714645558, 1247036630

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 8*a(n-3) - 13*a(n-4) + 12*a(n-5) -8*a(n-6) +8*a(n-7) -4*a(n-8) for n>13.

Empirical g.f.: x^2*(6 + 107*x - 174*x^2 + 171*x^3 - 548*x^4 + 441*x^5 - 308*x^6 + 519*x^7 - 92*x^8 + 34*x^9 - 28*x^10 - 32*x^11) / ((1 - x)^2*(1 - x - 2*x^3)^2). - Colin Barker, Feb 19 2019

Example

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

Crossrefs

Row 3 of A281400.

Sequence in context: A077031 A302770 A337971 * A137038 A024276 A137037

Adjacent sequences: A281399 A281400 A281401 * A281403 A281404 A281405

Keyword

nonn

Author

R. H. Hardin, Jan 21 2017

Status

approved