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A262844 Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

%I A262844 #10 Jun 11 2024 09:44:46
%S A262844 6,34,132,396,1264,3962,11886,35914,108556,325668,976552,2931922,
%T A262844 8795766,26370674,79104084,237312252,711756448,2135076202,6405228606,
%U A262844 19214238554,57640739420,172922218260,518757049560,1556255741762,4668767225286
%N A262844 Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.
%C A262844 Column 2 of A262849.
%H A262844 R. H. Hardin, <a href="/A262844/b262844.txt">Table of n, a(n) for n = 1..210</a>
%F A262844 Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) -68*a(n-4) +68*a(n-5) -162*a(n-6) +444*a(n-7) -444*a(n-8) +644*a(n-9) -1244*a(n-10) +1244*a(n-11) -1277*a(n-12) +1376*a(n-13) -1376*a(n-14) +1032*a(n-15).
%e A262844 Some solutions for n=4
%e A262844 ..1..1..1..0....1..1..1..0....1..1..1..0....0..0..0..0....0..0..0..0
%e A262844 ..0..1..1..1....0..0..0..0....1..1..1..0....0..0..0..0....0..0..0..0
%e A262844 ..0..1..1..1....0..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A262844 ..1..1..1..0....1..1..1..0....0..1..1..1....1..1..1..0....1..1..1..0
%e A262844 ..0..0..0..0....1..1..1..0....0..0..0..0....0..1..1..1....0..0..0..0
%e A262844 ..0..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1
%t A262844 v = Select[Tuples[{0, 1}, 4], Mod[FromDigits[#, 2], 7] == 0 &];
%t A262844 a[n_] := a[n] = Length[Select[Tuples[v, n + 2], !AnyTrue[Transpose[#], Mod[FromDigits[#, 2], 7] == 0 &] &]];
%t A262844 Table[a[n], {n, 1, 10}] (* _Robert P. P. McKone_, Jun 09 2024 *)
%Y A262844 Cf. A262849.
%K A262844 nonn
%O A262844 1,1
%A A262844 _R. H. Hardin_, Oct 03 2015