A269202 - OEIS

%I #8 Jan 20 2019 08:56:32

%S 16,180,1284,9612,68052,472044,3212820,21562476,143085588,940780908,

%T 6138286356,39791327340,256517615124,1645723601772,10514049071892,

%U 66922539204204,424564703856660,2685565034934636,16942451080369428

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

%H R. H. Hardin, <a href="/A269202/b269202.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4).

%F Conjectures from _Colin Barker_, Jan 20 2019: (Start)

%F G.f.: 4*x*(4 + 5*x - 77*x^2 + 18*x^3) / ((1 + x)^2*(1 - 6*x)^2).

%F a(n) = (6*(-678*(-1)^n+335*6^n) + 56*(144*(-1)^n+25*6^n)*n) / 1029.

%F (End)

%e Some solutions for n=4:

%e ..2..3..2..0. .1..0..0..0. .3..0..2..3. .0..3..3..1. .0..2..3..2

%e ..2..3..1..1. .0..0..2..1. .2..2..2..0. .1..1..3..1. .3..1..0..1

%Y Row 2 of A269201.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 20 2016