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
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
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..2000 (210 terms from R. H. Hardin)
Crossrefs
Column 2 of A245995.
Programs
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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
Comments