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A225344 Number of nX8 -1,1 arrays such that the sum over i=1..n,j=1..8 of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute 8-across galley oarsmen left-right at n fore-aft positions so that there are no turning moments on the ship).

%I A225344 #6 Jun 02 2025 08:33:17
%S A225344 1,1,5,27,171,1081,7261,50659,364051,2676331,20044255,152452967,
%T A225344 1174757541,9154016699,72023900129,571498084391,4568690484153,
%U A225344 36765944370729,297627015600415,2422216988266317,19808260648181603
%N A225344 Number of nX8 -1,1 arrays such that the sum over i=1..n,j=1..8 of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute 8-across galley oarsmen left-right at n fore-aft positions so that there are no turning moments on the ship).
%C A225344 Column 8 of A225345
%H A225344 R. H. Hardin, <a href="/A225344/b225344.txt">Table of n, a(n) for n = 1..97</a>
%e A225344 Some solutions for n=4
%e A225344 .-1.-1.-1.-1..1..1..1..1...-1.-1.-1.-1..1..1..1..1...-1.-1.-1.-1.-1.-1..1..1
%e A225344 .-1.-1..1..1..1..1..1..1...-1.-1.-1.-1.-1.-1..1..1...-1.-1..1..1..1..1..1..1
%e A225344 .-1.-1.-1.-1.-1.-1.-1.-1....1..1..1..1..1..1..1..1...-1.-1..1..1..1..1..1..1
%e A225344 .-1.-1..1..1..1..1..1..1...-1.-1.-1.-1.-1.-1..1..1...-1.-1.-1.-1.-1.-1..1..1
%K A225344 nonn
%O A225344 1,3
%A A225344 _R. H. Hardin_ May 05 2013