A296309 - OEIS

%I #8 Feb 22 2019 18:55:23

%S 1,4,7,10,23,45,76,150,293,532,1010,1942,3625,6833,13005,24499,46186,

%T 87489,165230,311809,589569,1114002,2103636,3975125,7511104,14188028,

%U 26805754,50647041,95680777,180765515,341525717,645225728,1218995503

%N Number of n X 4 0..1 arrays with each 1 adjacent to 3 or 6 king-move neighboring 1s.

%H R. H. Hardin, <a href="/A296309/b296309.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 4*a(n-3) - a(n-4) - 2*a(n-6).

%F Empirical g.f.: x*(1 + 3*x + 3*x^2 - x^3 - 2*x^4 - 2*x^5) / (1 - x - 4*x^3 + x^4 + 2*x^6). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 4 of A296313.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 10 2017