cp's OEIS Frontend

A269290 Number of 2 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

%I A269290 #8 Jan 21 2019 09:24:48
%S A269290 16,216,2124,19188,164556,1363572,11026764,87559668,685523916,
%T A269290 5306911092,40706083404,309846524148,2343253251276,17623065834612,
%U A269290 131903512372044,983118947312628,7300393156146636,54032675767734132,398738196097092684
%N A269290 Number of 2 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.
%H A269290 R. H. Hardin, <a href="/A269290/b269290.txt">Table of n, a(n) for n = 1..210</a>
%F A269290 Empirical: a(n) = 14*a(n-1) - 49*a(n-2) for n>4.
%F A269290 Conjectures from _Colin Barker_, Jan 21 2019: (Start)
%F A269290 G.f.: 4*x*(4 - 2*x - 29*x^2 + 9*x^3) / (1 - 7*x)^2.
%F A269290 a(n) = 36 * 7^(n-4) * (120*n+53) for n>2.
%F A269290 (End)
%e A269290 Some solutions for n=4:
%e A269290 ..0..0..2..1. .1..0..1..3. .1..3..2..2. .2..0..2..2. .3..1..3..2
%e A269290 ..2..2..3..3. .1..1..2..2. .3..2..2..0. .1..0..3..1. .0..3..2..0
%Y A269290 Row 2 of A269289.
%K A269290 nonn
%O A269290 1,1
%A A269290 _R. H. Hardin_, Feb 21 2016