cp's OEIS Frontend

A183981 1/4 the number of (n+1) X 5 binary arrays with all 2 X 2 subblock sums the same.

%I A183981 #11 Aug 31 2024 15:40:09
%S A183981 15,17,20,26,36,56,92,164,300,572,1100,2156,4236,8396,16652,33164,
%T A183981 66060,131852,263180,525836,1050636,2100236,4198412,8394764,16785420,
%U A183981 33566732,67125260,134242316,268468236,536920076,1073807372,2147581964,4295098380
%N A183981 1/4 the number of (n+1) X 5 binary arrays with all 2 X 2 subblock sums the same.
%C A183981 Column 4 of A183986.
%H A183981 R. H. Hardin, <a href="/A183981/b183981.txt">Table of n, a(n) for n = 1..200</a>
%H A183981 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183981 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A183981 Conjectures from _Colin Barker_, Apr 08 2018: (Start)
%F A183981 G.f.: x*(15 - 28*x - 31*x^2 + 56*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183981 a(n) = 3*2^(n/2-1) + 2^(n-1) + 12 for n even.
%F A183981 a(n) = 2^(n-1) + 2^((n+1)/2) + 12 for n odd.
%F A183981 (End)
%F A183981 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183981 Some solutions for 7 X 5:
%e A183981 ..0..1..0..1..0....0..0..0..0..1....0..1..0..1..0....0..1..0..1..0
%e A183981 ..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0
%e A183981 ..0..1..0..1..0....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1
%e A183981 ..1..1..1..1..1....1..0..1..0..0....1..0..1..0..1....0..0..0..0..0
%e A183981 ..1..0..1..0..1....0..0..0..0..1....0..1..0..1..0....1..0..1..0..1
%e A183981 ..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0
%e A183981 ..1..0..1..0..1....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1
%Y A183981 Cf. A183986.
%K A183981 nonn
%O A183981 1,1
%A A183981 _R. H. Hardin_, Jan 08 2011