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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A245995.

Sequence in context: A246911 A323918 A039460 * A110829 A242237 A182465

Adjacent sequences: A245987 A245988 A245989 * A245991 A245992 A245993

Keyword

nonn

Author

R. H. Hardin, Aug 09 2014

Status

approved