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A262912 Number of (n+1)X(3+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 A262912 #8 Aug 12 2019 02:24:30
%S A262912 1,6,15,53,318,1207,5797,34782,189135,1089701,6538206,38547751,
%T A262912 229660021,1377960126,8242589055,49395098933,296370593598,
%U A262912 1777250964247,10661181588037,63967089528222,383764138693935,2302493636842181
%N A262912 Number of (n+1)X(3+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.
%C A262912 Column 3 of A262917.
%H A262912 R. H. Hardin, <a href="/A262912/b262912.txt">Table of n, a(n) for n = 1..210</a>
%H A262912 Robert Israel, <a href="/A262912/a262912.pdf">Maple-assisted proof of empirical formula for A262912</a>
%F A262912 Empirical: a(n) = 8*a(n-1) -16*a(n-2) +104*a(n-3) -640*a(n-4) +1280*a(n-5) -3830*a(n-6) +15280*a(n-7) -30560*a(n-8) +58240*a(n-9) -99200*a(n-10) +198400*a(n-11) -283209*a(n-12) -115128*a(n-13) +230256*a(n-14) -345384*a(n-15).
%F A262912 Empirical formula verified: see link. - _Robert Israel_, Aug 12 2019
%e A262912 Some solutions for n=4
%e A262912 ..1..1..0..0....0..0..0..0....0..1..1..0....0..0..0..0....0..1..1..0
%e A262912 ..1..1..1..1....0..0..0..0....1..0..0..1....0..1..1..0....0..0..0..0
%e A262912 ..1..1..1..1....0..0..0..0....1..1..1..1....0..1..1..0....0..1..1..0
%e A262912 ..0..0..1..1....0..0..0..0....1..0..0..1....0..1..1..0....0..0..0..0
%e A262912 ..0..0..0..0....0..0..0..0....0..1..1..0....0..0..0..0....0..1..1..0
%Y A262912 Cf. A262917.
%K A262912 nonn
%O A262912 1,2
%A A262912 _R. H. Hardin_, Oct 04 2015