A245989 Number of length n 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.

1, 3, 6, 8, 12, 18, 26, 38, 56, 82, 120, 176, 258, 378, 554, 812, 1190, 1744, 2556, 3746, 5490, 8046, 11792, 17282, 25328, 37120, 54402, 79730, 116850, 171252, 250982, 367832, 539084, 790066, 1157898, 1696982, 2487048, 3644946, 5341928, 7828976, 11473922

Offset

0,2

Comments

Also, number of length n ternary words with no pair of equal consecutive letters and avoiding the subwords 010, 101, 020, 202. - Miquel A. Fiol, Dec 22 2023

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (210 terms from R. H. Hardin)

Formula

a(n) = a(n-1) + a(n-3) for n>=5.

G.f.: (x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3). - Colin Barker, Nov 05 2018

Example

Some solutions for n=12:
  0  1  0  1  1  0  2  2  0  2  0  2  0  0  0  1
  0  2  1  2  0  0  1  2  1  1  0  2  0  0  1  2
  0  2  0  2  0  1  2  1  0  2  0  2  0  0  0  2
  0  2  0  1  0  0  2  2  0  2  1  1  1  1  0  1
  0  1  1  2  0  0  2  2  0  2  0  2  0  0  0  2
  0  2  0  2  1  1  2  1  1  1  0  2  0  0  0  2
  0  2  0  2  0  0  1  2  0  2  0  2  0  0  1  2
  0  2  0  2  0  0  2  2  0  2  0  2  0  0  0  2
  0  1  1  2  1  1  2  1  0  2  0  1  1  0  0  1
  0  2  0  1  0  0  2  2  0  2  0  2  0  0  0  2
  0  2  0  2  0  0  2  2  0  1  1  2  0  0  0  2
  0  2  0  2  1  0  1  1  0  2  0  1  0  0  1  2

Mathematica

gf=(x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3); Table[SeriesCoefficient[gf, {x, 0, n}], {n, 0, 40}]  (* James C. McMahon, Dec 30 2023 *)

Crossrefs

Column 2 of A245995.

Sequence in context: A288218 A212984 A006048 * A350928 A049827 A186736

Adjacent sequences: A245986 A245987 A245988 * A245990 A245991 A245992

Keyword

nonn,easy

Author

R. H. Hardin, Aug 09 2014

Extensions

Edited by Alois P. Heinz, Dec 30 2023

Status

approved