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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.
1
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
1,2
COMMENTS
Column 1 of A232589.
LINKS
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
EXAMPLE
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
CROSSREFS
Sequence in context: A317536 A203175 A102477 * A018074 A288465 A000067
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 26 2013
STATUS
approved