A193644 Number of arrays of -4..4 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.

1, 9, 25, 105, 369, 1393, 5105, 18937, 69897, 258521, 955361, 3531745, 13054177, 48254185, 178365177, 659309641, 2437064529, 9008352081, 33298400977, 123083978969, 454966715881, 1681735706553, 6216355687361, 22978092329921

Offset

1,2

Comments

Column 4 of A193648.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) +a(n-3).

Empirical g.f.: x*(1 + 7*x + x^2) / (1 - 2*x - 6*x^2 - x^3). - Colin Barker, May 04 2018

Example

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

Crossrefs

Cf. A193648.

Sequence in context: A147475 A146674 A083672 * A083100 A084058 A108570

Adjacent sequences: A193641 A193642 A193643 * A193645 A193646 A193647

Keyword

nonn

Author

R. H. Hardin, Aug 02 2011

Status

approved