A245990 Number of length n+2 0..3 arrays with no pair in any consecutive three terms totalling exactly 3.

28, 68, 164, 396, 956, 2308, 5572, 13452, 32476, 78404, 189284, 456972, 1103228, 2663428, 6430084, 15523596, 37477276, 90478148, 218433572, 527345292, 1273124156, 3073593604, 7420311364, 17914216332, 43248744028, 104411704388

Offset: 1

Author

R. H. Hardin, Aug 09 2014

Keywords

• nonn

Examples

			Some solutions for n=10:
  3  2  1  1  2  1  1  2  0  2  3  0  1  3  3  0
  3  2  1  0  2  3  0  2  2  3  2  0  3  1  2  2
  3  3  3  0  3  1  0  2  0  2  2  0  1  1  2  0
  3  2  1  1  3  1  0  2  0  3  2  1  3  3  3  2
  3  3  1  1  1  1  0  0  0  3  0  1  1  1  3  2
  2  3  0  0  3  3  2  2  1  2  2  1  1  3  2  2
  2  2  1  0  1  1  2  2  1  3  0  1  1  3  2  2
  2  3  1  1  3  3  3  2  1  3  2  0  3  3  3  0
  3  3  1  1  3  1  3  2  3  3  0  0  1  2  2  0
  2  1  0  3  3  1  2  3  3  2  2  0  1  3  2  1
  3  1  0  1  3  0  3  3  2  2  2  0  0  3  3  1
  2  0  1  3  3  0  2  1  3  0  3  1  0  1  2  3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 3 of A245995.

Essentially 4 times A001333.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2).

Conjectures from Colin Barker, Nov 05 2018: (Start)

G.f.: 4*x*(7 + 3*x) / (1 - 2*x - x^2).

a(n) = sqrt(2)*((1-sqrt(2))^n*(-4+3*sqrt(2)) + (1+sqrt(2))^n*(4+3*sqrt(2))).

(End)