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A303714 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero. 1

%I #8 May 17 2023 12:14:53

%S 3,3,5,8,14,24,40,68,116,196,332,564,956,1620,2748,4660,7900,13396,

%T 22716,38516,65308,110740,187772,318388,539868,915412,1552188,2631924,

%U 4462748,7567124,12830972,21756468,36890716,62552660,106065596,179847028

%N Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

%C Column 3 of A303719.

%H R. H. Hardin, <a href="/A303714/b303714.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 3*x-x^2*(3+2*x+3*x^2)/(-1+x+2*x^3). - _R. J. Mathar_, Apr 30 2018

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A303719.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 29 2018

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)