A225314 - OEIS

%I #4 May 05 2013 06:40:52

%S 8,87,474,1787,5304,13333,29638,60007,112790,199669,336342,543465,

%T 847456,1281681,1887330,2714817,3824812,5289809,7195252,9641399,

%U 12744472,16638757,21477906,27437211,34714980,43535143,54148610,66836145,81909858

%N Number of 7Xn -1,1 arrays such that the sum over i=1..7,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 7 positions 1..n distance from the hinge of a south-pointing gate without turning the gate)

%C Row 7 of A225310

%H R. H. Hardin, <a href="/A225314/b225314.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-2) +2*a(n-3) -3*a(n-4) -5*a(n-5) +4*a(n-7) +a(n-8) -2*a(n-9) +a(n-10) +3*a(n-11) -3*a(n-13) -a(n-14) +2*a(n-15) -a(n-16) -4*a(n-17) +5*a(n-19) +3*a(n-20) -2*a(n-21) -3*a(n-22) +a(n-24)

%e Some solutions for n=4

%e ..1..1..1..1...-1..1..1..1...-1.-1..1..1...-1.-1.-1.-1...-1.-1.-1.-1

%e .-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1.-1

%e .-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1

%e ..1..1..1..1...-1.-1.-1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1

%e .-1.-1.-1.-1...-1..1..1..1...-1.-1..1..1...-1.-1.-1..1....1..1..1..1

%e ..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1....1..1..1..1

%e .-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1.-1

%K nonn

%O 1,1

%A _R. H. Hardin_ May 05 2013