A225315 Number of 8Xn -1,1 arrays such that the sum over i=1..8,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 8 positions 1..n distance from the hinge of a south-pointing gate without turning the gate)

14, 217, 1576, 7445, 26498, 77721, 197440, 449693, 939130, 1828785, 3360554, 5882479, 9878430, 16007047, 25142264, 38426053, 57321356, 83680907, 119814040, 168573865, 233439470, 318623729, 429172318, 571094583, 751480676, 978657917

Offset

1,1

Comments

Row 8 of A225310

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-7) -a(n-9) +a(n-11) +2*a(n-12) +a(n-13) +a(n-15) -a(n-16) -a(n-17) -2*a(n-18) -a(n-19) -a(n-20) +a(n-21) +a(n-23) +2*a(n-24) +a(n-25) -a(n-27) -a(n-29) -a(n-31) +a(n-34) +a(n-35) -a(n-36)

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
.-1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1...-1.-1..1..1
.-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1.-1.-1..1...-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

Sequence in context: A240781 A353146 A113894 * A292041 A319114 A145269

Adjacent sequences: A225312 A225313 A225314 * A225316 A225317 A225318

Keyword

nonn

Author

R. H. Hardin May 05 2013

Status

approved