A183981 - OEIS

%I #11 Aug 31 2024 15:40:09

%S 15,17,20,26,36,56,92,164,300,572,1100,2156,4236,8396,16652,33164,

%T 66060,131852,263180,525836,1050636,2100236,4198412,8394764,16785420,

%U 33566732,67125260,134242316,268468236,536920076,1073807372,2147581964,4295098380

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

%C Column 4 of A183986.

%H R. H. Hardin, <a href="/A183981/b183981.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).

%F Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

%F Conjectures from _Colin Barker_, Apr 08 2018: (Start)

%F G.f.: x*(15 - 28*x - 31*x^2 + 56*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2-1) + 2^(n-1) + 12 for n even.

%F a(n) = 2^(n-1) + 2^((n+1)/2) + 12 for n odd.

%F (End)

%F The above empirical formula is correct. See note from Andrew Howroyd in A183986.

%e Some solutions for 7 X 5:

%e ..0..1..0..1..0....0..0..0..0..1....0..1..0..1..0....0..1..0..1..0

%e ..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0

%e ..0..1..0..1..0....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1

%e ..1..1..1..1..1....1..0..1..0..0....1..0..1..0..1....0..0..0..0..0

%e ..1..0..1..0..1....0..0..0..0..1....0..1..0..1..0....1..0..1..0..1

%e ..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0

%e ..1..0..1..0..1....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1

%Y Cf. A183986.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011