A193703 Number of arrays of -1..1 integers x(1..n) with every x(i) in a subsequence of length 1, 2, 3 or 4 with sum zero.

1, 3, 9, 27, 73, 195, 515, 1357, 3585, 9479, 25069, 66307, 175381, 463859, 1226827, 3244745, 8581777, 22697291, 60030393, 158769987, 419919089, 1110613203, 2937379387, 7768859149, 20547285345, 54344006943, 143730475357, 380142185163

Offset

1,2

Comments

Column 1 of A193710.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4) +3*a(n-6) +4*a(n-7).

Empirical g.f.: x*(1 + x)^2*(1 - x + 3*x^2 - x^3 + 4*x^4) / (1 - 2*x - x^2 - 2*x^3 + x^4 - 3*x^6 - 4*x^7). - Colin Barker, May 04 2018

Example

Some solutions for n=6:
   1  0  1  0 -1 -1  0  0  1  0 -1 -1  0 -1  1  0
  -1 -1 -1  1  1  1  1  0 -1  0  0  1  0  1 -1 -1
   0  1 -1  0  1  1 -1 -1  0  0  1  1  1  0  0  1
   1  1  1 -1  0 -1 -1  1  0 -1 -1 -1 -1  1 -1  0
   0 -1  1  0  0  0  1 -1  0  1  0  1  1  0  0  1
   0  1  0  0 -1  0 -1  0  0  0  0 -1 -1 -1  1 -1

Crossrefs

Cf. A193710.

Sequence in context: A042938 A206604 A084707 * A289658 A180238 A289693

Adjacent sequences: A193700 A193701 A193702 * A193704 A193705 A193706

Keyword

nonn

Author

R. H. Hardin, Aug 02 2011

Status

approved