A183980 1/4 the number of (n+1) X 4 binary arrays with all 2 X 2 subblock sums the same.

9, 11, 14, 20, 30, 50, 86, 158, 294, 566, 1094, 2150, 4230, 8390, 16646, 33158, 66054, 131846, 263174, 525830, 1050630, 2100230, 4198406, 8394758, 16785414, 33566726, 67125254, 134242310, 268468230, 536920070, 1073807366, 2147581958, 4295098374

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn

Comments

Column 3 of A183986.

Examples

			Some solutions for 5 X 4.
..0..1..0..1....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
..1..0..1..0....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
..0..1..0..1....1..1..1..1....0..0..1..1....0..1..0..1....1..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4).

Crossrefs

Cf. A183986.

Formula

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

Conjectures from Colin Barker, Apr 07 2018: (Start)

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

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

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

(End)

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