A184030 1/16 the number of (n+1) X (n+1) 0..3 arrays with all 2 X 2 subblocks having the same four values.

16, 40, 82, 166, 322, 634, 1234, 2434, 4786, 9490, 18802, 37426, 74482, 148594, 296434, 592114, 1182706, 2363890, 4724722, 9446386, 18886642, 37767154, 75522034, 151031794, 302039026, 604053490, 1208057842, 2416066546, 4832034802, 9663971314, 19327746034, 38655295474

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn
• easy

Examples

			Some solutions for 4X4
..1..3..1..1....3..0..3..0....2..2..2..2....0..0..0..0....1..0..0..0
..1..1..1..3....0..1..0..1....1..3..1..3....2..2..2..2....0..2..1..2
..1..3..1..1....0..3..0..3....2..2..2..2....0..0..0..0....1..0..0..0
..1..1..1..3....1..0..1..0....3..1..3..1....2..2..2..2....0..2..1..2
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Crossrefs

Diagonal of A184039.

Programs

PARI

Vec(2*(8 - 4*x - 19*x^2 + 8*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^30)) \\ Andrew Howroyd, Mar 09 2024

Formula

From Andrew Howroyd, Mar 09 2024: (Start)

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

G.f.: 2*x*(8 - 4*x - 19*x^2 + 8*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)

Extensions

a(14) onwards from Andrew Howroyd, Mar 09 2024