A255111 Number of length n+4 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
243, 622, 1137, 1905, 2951, 4338, 6141, 8448, 11361, 14997, 19489, 24987, 31659, 39692, 49293, 60690, 74133, 89895, 108273, 129589, 154191, 182454, 214781, 251604, 293385, 340617, 393825, 453567, 520435, 595056, 678093, 770246, 872253, 984891
Offset: 1
Keywords
Examples
Some solutions for n=4: 1 1 0 0 2 2 1 2 0 0 2 2 1 2 0 0 1 1 0 2 0 0 2 0 0 2 2 2 2 0 1 2 1 2 0 1 1 0 2 2 2 1 2 2 0 0 1 1 0 2 1 1 1 0 1 2 2 1 2 2 0 0 2 2 0 2 2 1 1 1 2 2 2 1 1 2 2 0 2 2 0 2 2 2 2 2 2 2 2 2 1 1 2 1 0 2 1 2 0 0 1 2 2 0 2 2 2 1 2 2 2 2 0 2 0 0 1 2 0 2 0 2 2 2 1 1 2 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A255107.
Formula
Empirical: a(n) = (1/120)*n^5 + (7/24)*n^4 + (85/24)*n^3 + (1505/24)*n^2 + (2809/20)*n + 30 for n>2.
Empirical g.f.: x*(243 - 836*x + 1050*x^2 - 447*x^3 - 219*x^4 + 339*x^5 - 156*x^6 + 27*x^7) / (1 - x)^6. - Colin Barker, Jan 24 2018
Comments