A193645 Number of arrays of -5..5 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.

1, 11, 31, 151, 561, 2361, 9361, 38171, 153591, 621911, 2510721, 10150321, 41008321, 165729931, 669676751, 2706201271, 10935546481, 44190379881, 178571332881, 721601251291, 2915963545511, 11783308434231, 47615926483841

Offset

1,2

Comments

Column 5 of A193648.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) +8*a(n-2) +a(n-3).

Empirical g.f.: x*(1 + 9*x + x^2) / (1 - 2*x - 8*x^2 - x^3). - Colin Barker, May 04 2018

Example

Some solutions for n=6:
  -5 -5  0  4 -5  5  4  0 -4 -5  0  0  0  2  1  1
   5  5  3 -4  5 -5 -4  5  4  5  0 -2  2 -2 -1 -1
   2 -1 -3  4  5 -3  1 -5 -4 -5 -2  2 -2  5  1  3
  -2  1 -4  1 -5  3 -1  5  1  5  2 -2  0 -5 -3 -3
  -3  5  4 -1  4  0 -1 -2 -1 -4  3 -3  0  1  3 -1
   3 -5  0  1 -4  0  1  2  0  4 -3  3  0 -1 -3  1

Crossrefs

Cf. A193648.

Sequence in context: A049090 A181150 A094622 * A190781 A001604 A144727

Adjacent sequences: A193642 A193643 A193644 * A193646 A193647 A193648

Keyword

nonn

Author

R. H. Hardin, Aug 02 2011

Status

approved