A183628 Number of (n+1)X6 0..2 arrays with every 2x2 subblock summing to 4

859, 1125, 1675, 2829, 5299, 10725, 23035, 52029, 123139, 304725, 785995, 2102829, 5799379, 16381125, 47110555, 137267229, 403674019, 1194767925, 3551796715, 10590377229, 31641107059, 94663273125, 283469724475, 849368984829

Offset

1,1

Comments

Column 5 of A183632

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Maple-assisted proof of empirical formula

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

Empirical: a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3)

From Robert Israel, Mar 30 2018: (Start)

Empirical formula confirmed - see link.

G.f.: (859*x-4029*x^2+4374*x^3)/(1-6*x+11*x^2-6*x^3).

a(n)=124*2^n+3*3^n+602. (End)

Example

Some solutions for 3X6
..2..2..0..1..0..1....2..1..2..0..0..0....1..1..1..0..2..0....1..2..0..1..0..1
..0..0..2..1..2..1....0..1..0..2..2..2....1..1..1..2..0..2....0..1..1..2..1..2
..2..2..0..1..0..1....2..1..2..0..0..0....0..2..0..1..1..1....1..2..0..1..0..1

Maple

seq(124*2^n+3*3^n+602, n=1..30); # Robert Israel, Apr 02 2018

Crossrefs

Sequence in context: A284074 A345548 A345801 * A187281 A108822 A278156

Adjacent sequences: A183625 A183626 A183627 * A183629 A183630 A183631

Keyword

nonn

Author

R. H. Hardin Jan 06 2011

Status

approved