cp's OEIS Frontend

A262267 Number of (n+2) X (1+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.

%I A262267 #8 Feb 21 2018 19:19:39
%S A262267 2,4,7,13,26,52,103,205,410,820,1639,3277,6554,13108,26215,52429,
%T A262267 104858,209716,419431,838861,1677722,3355444,6710887,13421773,
%U A262267 26843546,53687092,107374183,214748365,429496730,858993460,1717986919,3435973837
%N A262267 Number of (n+2) X (1+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.
%C A262267 Column 1 of A262274.
%H A262267 R. H. Hardin, <a href="/A262267/b262267.txt">Table of n, a(n) for n = 1..210</a>
%F A262267 Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 2*a(n-4).
%F A262267 Conjectures from _Colin Barker_, Feb 21 2018: (Start)
%F A262267 G.f.: x*(2 - 2*x + x^2 - 2*x^3) / ((1 - x)*(1 - 2*x)*(1 + x^2)).
%F A262267 a(n) = 1/2 + 2^(2+n)/5 - (1/20-i/20)*((1+2*i)*(-i)^n + (2+i)*i^n) where i=sqrt(-1).
%F A262267 (End)
%e A262267 Some solutions for n=4:
%e A262267 ..0..0..0....0..0..0....1..0..1....1..0..1....0..0..0....0..0..0....0..0..0
%e A262267 ..1..0..1....0..0..0....0..0..0....1..0..1....0..0..0....0..0..0....1..0..1
%e A262267 ..1..0..1....0..0..0....1..0..1....0..0..0....1..0..1....0..0..0....1..0..1
%e A262267 ..1..0..1....1..0..1....0..0..0....1..0..1....1..0..1....0..0..0....0..0..0
%e A262267 ..1..0..1....0..0..0....0..0..0....1..0..1....1..0..1....0..0..0....0..0..0
%e A262267 ..0..0..0....1..0..1....0..0..0....1..0..1....1..0..1....0..0..0....1..0..1
%Y A262267 Cf. A262274.
%K A262267 nonn
%O A262267 1,1
%A A262267 _R. H. Hardin_, Sep 17 2015