A232582 Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
0, 2, 4, 6, 10, 18, 32, 56, 98, 172, 302, 530, 930, 1632, 2864, 5026, 8820, 15478, 27162, 47666, 83648, 146792, 257602, 452060, 793310, 1392162, 2443074, 4287296, 7523680, 13203138, 23169892, 40660326, 71353898, 125217362, 219741152, 385618840
Offset: 1
Keywords
Examples
Some solutions for n=7: 2 1 0 1 2 1 0 1 0 1 0 1 0 1 2 1 0 1 2 1 0 1 2 1 0 1 2 0 2 1 2 0 2 1 0 2 2 0 0 1 2 0 0 1 2 0 1 2 0 2 1 2 0 1 1 0 1 2 2 0 1 2 2 1 1 2 1 0 1 0 0 1 2 0 1 2 0 1 1 2 1 0 0 1 0 1 2 1 2 1 2 0 1 2 1 0 2 1 1 0 1 2 2 0 2 1 0 2 0 1 1 2 0 1 1 2 0 2 2 1 1 0 1 2 0 2 1 0 2 0 1 0 2 0 1 0 1 0 0 2 1 2 1 0 1 0 1 2 1 2 1 2 1 2 1 2 1 2 1 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) = 2*A005314(n-1).
Empirical: G.f.: -2*x^2 / ( -1+2*x-x^2+x^3 ). - R. J. Mathar, Nov 23 2014
Theorem: a(n) = Sum_{j=1..floor((n-2)/3)} 2* Hypergeometric2F1([2+3*j-n,-(2j+1)], [1], 1). - Richard Turk, Oct 22 2019
Comments