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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).
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 05 2013
STATUS
approved