A225312 Number of 5 X n -1,1 arrays such that the sum over i=1..5,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 5 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

0, 15, 0, 113, 0, 427, 0, 1165, 0, 2591, 0, 5053, 0, 8947, 0, 14759, 0, 23017, 0, 34347, 0, 49409, 0, 68967, 0, 93813, 0, 124851, 0, 163005, 0, 209317, 0, 264843, 0, 330765, 0, 408271, 0, 498681, 0, 603315, 0, 723633, 0, 861087, 0, 1017275, 0, 1193781, 0

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-2) - 2*a(n-4) - 2*a(n-6) + 4*a(n-8) - 4*a(n-10) + 2*a(n-12) + 2*a(n-14) - 3*a(n-16) + a(n-18).

Empirical g.f.: x^2*(15 + 68*x^2 + 118*x^4 + 140*x^6 + 116*x^8 + 72*x^10 + 14*x^12 - 2*x^14 + x^16) / ((1 - x)^5*(1 + x)^5*(1 + x^2)^2*(1 + x^4)). - Colin Barker, Sep 05 2018

Example

Some solutions for n=4:
..1..1..1..1....1..1..1..1...-1..1..1..1....1..1..1..1...-1.-1.-1..1
.-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1.-1.-1..1...-1..1..1..1
.-1.-1.-1.-1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1.-1.-1..1....1..1..1..1...-1.-1.-1.-1....1..1..1..1...-1..1..1..1
..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1.-1..1

Crossrefs

Row 5 of A225310.

Sequence in context: A277929 A303231 A225346 * A370335 A333845 A015908

Adjacent sequences: A225309 A225310 A225311 * A225313 A225314 A225315

Keyword

nonn

Author

R. H. Hardin, May 05 2013

Status

approved