A251367 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 1, 2, 3, 4, 5, 6, or 7.

695, 17969, 464393, 12002283, 310199103, 8017100977, 207202101873, 5355141623323, 138403720518311, 3577046360518609, 92448820142650873, 2389341228591410219, 61752562096926105327, 1595995950642355498897

Offset: 1

Author

R. H. Hardin, Dec 01 2014

Keywords

• nonn

Comments

Column 2 of A251373.

Examples

			Some solutions for n=2:
  2 1 1   2 0 2   0 2 1   2 2 2   0 0 2   0 0 2   0 0 2
  0 0 0   1 0 0   1 0 1   0 1 1   1 1 2   1 2 1   1 1 1
  1 2 2   2 0 1   1 2 1   2 0 2   0 0 1   1 0 1   0 1 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical formula
• Index entries for linear recurrences with constant coefficients, signature (24,49,-34).

Programs

Maple

f:= gfun:-rectoproc({a(n) = 24*a(n-1) +49*a(n-2) -34*a(n-3),a(1)=695,a(2)=17969, a(3)=464393},a(n),remember):
map(f, [$1..30]); # Robert Israel, Mar 19 2018

Formula

Empirical: a(n) = 24*a(n-1) + 49*a(n-2) - 34*a(n-3).

From Robert Israel, Mar 19 2018: (Start)

Empirical formula verified: see link.

G.f.: (695*x+1289*x^2-918*x^3)/(1-24*x-49*x^2+34*x^3). (End)