A183980 - OEIS

%I #15 Aug 31 2024 15:39:26

%S 9,11,14,20,30,50,86,158,294,566,1094,2150,4230,8390,16646,33158,

%T 66054,131846,263174,525830,1050630,2100230,4198406,8394758,16785414,

%U 33566726,67125254,134242310,268468230,536920070,1073807366,2147581958,4295098374

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

%C Column 3 of A183986.

%H R. H. Hardin, <a href="/A183980/b183980.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 07 2018: (Start)

%F G.f.: x*(9 - 16*x - 19*x^2 + 32*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

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

%F a(n) = 2^((n-5)/2+3) + 2^(n-1) + 6 for n odd.

%F (End)

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

%e Some solutions for 5 X 4.

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

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

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

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

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

%Y Cf. A183986.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011