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A262918 Number of (4+1) X (n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

%I A262918 #8 Jan 01 2019 08:43:55
%S A262918 5,9,53,137,853,2953,17333,71721,394325,1791209,9435253,44924617,
%T A262918 230950613,1126125513,5713545653,28200027881,142082597845,
%U A262918 705663892009,3542422689653,17650591452297,88436516562773,441384307595273
%N A262918 Number of (4+1) X (n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
%H A262918 R. H. Hardin, <a href="/A262918/b262918.txt">Table of n, a(n) for n = 1..210</a>
%F A262918 Empirical: a(n) = 7*a(n-1) + 11*a(n-2) - 147*a(n-3) + 99*a(n-4) + 777*a(n-5) - 1019*a(n-6) - 637*a(n-7) + 910*a(n-8).
%F A262918 Empirical g.f.: x*(5 - 26*x - 65*x^2 + 402*x^3 + 139*x^4 - 1510*x^5 + 273*x^6 + 910*x^7) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 5*x)*(1 - 7*x^2)*(1 - 13*x^2)). - _Colin Barker_, Jan 01 2019
%e A262918 Some solutions for n=4:
%e A262918 ..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..0..0..1..1
%e A262918 ..0..1..1..1..1....0..0..0..1..1....0..1..1..0..0....0..0..0..1..1
%e A262918 ..0..1..1..1..1....1..1..0..1..1....0..1..1..0..0....1..1..0..1..1
%e A262918 ..0..1..1..1..1....0..0..0..1..1....0..1..1..0..0....1..1..0..0..0
%e A262918 ..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....1..1..0..0..0
%Y A262918 Row 4 of A262917.
%K A262918 nonn
%O A262918 1,1
%A A262918 _R. H. Hardin_, Oct 04 2015