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A225349 Number of 9Xn -1,1 arrays such that the sum over i=1..9,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 9 fore-aft positions so that there are no turning moments on the ship).

%I A225349 #6 Jun 02 2025 08:33:44
%S A225349 0,181,0,6095,0,63121,0,364051,0,1478059,0,4749875,0,12917383,0,
%T A225349 30996867,0,67483509,0,135917019,0,256859575,0,460336079,0,788783775,
%U A225349 0,1300561813,0,2074066679,0,3212505371,0,4849371247,0,7154674999,0,10341975199,0
%N A225349 Number of 9Xn -1,1 arrays such that the sum over i=1..9,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 9 fore-aft positions so that there are no turning moments on the ship).
%C A225349 Row 9 of A225345
%H A225349 R. H. Hardin, <a href="/A225349/b225349.txt">Table of n, a(n) for n = 1..210</a>
%F A225349 Empirical: a(n) = 2*a(n-2) -a(n-6) -a(n-10) +a(n-12) -a(n-14) +a(n-18) +a(n-20) +a(n-24) -2*a(n-26) -2*a(n-32) +a(n-34) +a(n-38) +a(n-40) -a(n-44) +a(n-46) -a(n-48) -a(n-52) +2*a(n-56) -a(n-58)
%e A225349 Some solutions for n=4
%e A225349 .-1.-1..1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1
%e A225349 .-1.-1.-1.-1...-1.-1.-1.-1....1..1..1..1...-1.-1..1..1...-1.-1.-1..1
%e A225349 .-1.-1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1....1..1..1..1
%e A225349 ..1..1..1..1...-1.-1..1..1...-1.-1..1..1...-1.-1.-1.-1...-1..1..1..1
%e A225349 .-1.-1..1..1....1..1..1..1...-1.-1..1..1....1..1..1..1...-1.-1.-1.-1
%e A225349 .-1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1
%e A225349 .-1..1..1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1
%e A225349 .-1.-1.-1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1....1..1..1..1
%e A225349 .-1.-1.-1..1...-1.-1.-1..1....1..1..1..1...-1..1..1..1...-1.-1..1..1
%K A225349 nonn
%O A225349 1,2
%A A225349 _R. H. Hardin_ May 05 2013