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

1,1

Links

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

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

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

Crossrefs

Row 4 of A225310.

Sequence in context: A005581 A375279 A064468 * A241526 A074470 A216499

Adjacent sequences: A225308 A225309 A225310 * A225312 A225313 A225314

Keyword

nonn

Author

R. H. Hardin, May 05 2013

Status

approved