A225311 Number of 4 X n -1,1 arrays such that the sum over i=1..4,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 4 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

2, 7, 16, 31, 52, 83, 122, 175, 238, 317, 410, 523, 650, 801, 970, 1165, 1380, 1625, 1892, 2193, 2518, 2879, 3268, 3697, 4154, 4655, 5188, 5767, 6380, 7043, 7742, 8495, 9286, 10133, 11022, 11971, 12962, 14017, 15118, 16285, 17500, 18785, 20120, 21529, 22990

Offset: 1

Author

R. H. Hardin, May 05 2013

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 4 of A225310.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).

Empirical g.f.: x*(2 + 5*x + 7*x^2 + 8*x^3 + 5*x^4 + 4*x^5 + x^6 + 2*x^7 + x^8 - x^9) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 05 2018