A198620 - OEIS

A198620

Number of n X 1 0..5 arrays with values 0..5 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

%I #10 May 14 2018 14:16:49

%S 0,1,1,2,3,6,11,23,47,103,226,518,1200,2866,6939,17184,43133,110122,

%T 284485,744297,1965907,5240825,14072796,38039586,103368602,282201932,

%U 773327639,2126010274,5860104847,16188449006,44801184159,124173477355

%N Number of n X 1 0..5 arrays with values 0..5 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

%C Column 1 of A198627.

%H R. H. Hardin, <a href="/A198620/b198620.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) +a(n-2) -34*a(n-3) +20*a(n-4) +80*a(n-5) -51*a(n-6) -81*a(n-7) +31*a(n-8) +30*a(n-9) for n>10.

%F Empirical g.f.: x^2*(1 - 4*x - 4*x^2 + 26*x^3 + 3*x^4 - 54*x^5 - 5*x^6 + 37*x^7 + 11*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 5*x^2)). - _Colin Barker_, May 14 2018

%e All solutions for n=4:

%e ..0....0

%e ..0....1

%Y Cf. A198627.

%K nonn

%O 1,4

%A _R. H. Hardin_, Oct 27 2011