A281401 - OEIS

A281401

Number of 2 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.

%I #8 Feb 18 2019 20:04:36

%S 0,0,10,52,170,484,1296,3308,8222,19996,47894,113320,265560,617472,

%T 1426498,3277796,7497418,17082444,38791072,87831508,198365446,

%U 447006060,1005324158,2257048752,5059420328,11325490728,25320461706,56545544372

%N Number of 2 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.

%H R. H. Hardin, <a href="/A281401/b281401.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) - a(n-4) + 30*a(n-5) + 4*a(n-6) - 24*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>10.

%F Empirical g.f.: 2*x^3*(1 + 2*x - 2*x^3)*(5 - 4*x - 16*x^2 - 2*x^3 + 12*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)^2). - _Colin Barker_, Feb 18 2019

%e Some solutions for n=4:

%e ..0..1..0..1. .0..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..1..1

%e ..0..0..0..0. .0..1..0..0. .1..0..1..0. .1..0..1..0. .1..1..0..1

%Y Row 2 of A281400.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 21 2017