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

1,1

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).

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)

Example

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

Prog

(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

Crossrefs

Diagonal of A184039.

Sequence in context: A174321 A258258 A086046 * A350284 A182461 A205065

Adjacent sequences: A184027 A184028 A184029 * A184031 A184032 A184033

Keyword

nonn,easy

Author

R. H. Hardin, Jan 08 2011

Extensions

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

Status

approved