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A262421 Number of (2+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

%I A262421 #9 Dec 31 2018 11:27:10
%S A262421 5,4,45,114,709,2892,15293,72370,367125,1808844,9078925,45214674,
%T A262421 226307429,1130307532,5653140573,28257215730,141297157045,
%U A262421 706426855884,3532211260205,17660645718034,88303765183749,441515959527372
%N A262421 Number of (2+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.
%H A262421 R. H. Hardin, <a href="/A262421/b262421.txt">Table of n, a(n) for n = 1..210</a>
%F A262421 Empirical: a(n) = 5*a(n-1) + 12*a(n-2) - 60*a(n-3) - 39*a(n-4) + 195*a(n-5) + 28*a(n-6) - 140*a(n-7).
%F A262421 Empirical g.f.: x*(5 - 21*x - 35*x^2 + 141*x^3 + 34*x^4 - 140*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 5*x)*(1 - 7*x^2)). - _Colin Barker_, Dec 31 2018
%e A262421 Some solutions for n=4:
%e A262421 ..1..1..0..0..0....0..1..1..0..0....1..1..1..1..0....1..1..0..1..1
%e A262421 ..0..1..0..0..1....1..1..0..1..1....1..1..0..0..0....0..1..1..0..0
%e A262421 ..1..1..1..1..0....0..1..1..0..0....1..1..0..1..1....1..1..0..0..0
%Y A262421 Row 2 of A262420.
%K A262421 nonn
%O A262421 1,1
%A A262421 _R. H. Hardin_, Sep 22 2015