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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).

%I A225315 #6 Jun 02 2025 08:32:37
%S A225315 14,217,1576,7445,26498,77721,197440,449693,939130,1828785,3360554,
%T A225315 5882479,9878430,16007047,25142264,38426053,57321356,83680907,
%U A225315 119814040,168573865,233439470,318623729,429172318,571094583,751480676,978657917
%N 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).
%C A225315 Row 8 of A225310
%H A225315 R. H. Hardin, <a href="/A225315/b225315.txt">Table of n, a(n) for n = 1..210</a>
%F A225315 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)
%e A225315 Some solutions for n=4
%e A225315 ..1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1.-1...-1.-1..1..1
%e A225315 .-1.-1.-1.-1....1..1..1..1...-1.-1..1..1...-1.-1.-1..1....1..1..1..1
%e A225315 .-1.-1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1..1..1
%e A225315 .-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1.-1...-1..1..1..1...-1.-1.-1.-1
%e A225315 .-1.-1.-1..1...-1..1..1..1...-1..1..1..1...-1.-1.-1.-1...-1..1..1..1
%e A225315 .-1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1...-1.-1..1..1
%e A225315 .-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1.-1.-1..1...-1..1..1..1
%e A225315 ..1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1
%K A225315 nonn
%O A225315 1,1
%A A225315 _R. H. Hardin_ May 05 2013