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

1,2

Comments

Column 1 of A232589.

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

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

Adjacent sequences: A232579 A232580 A232581 * A232583 A232584 A232585

Keyword

nonn

Author

R. H. Hardin, Nov 26 2013

Status

approved