cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

R. H. Hardin, Aug 09 2014

Keywords

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

Examples

			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
		

Crossrefs

Column 2 of A245995.

Programs

  • 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 *)

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

Extensions

Edited by Alois P. Heinz, Dec 30 2023