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A225348 Number of 8Xn -1,1 arrays such that the sum over i=1..8,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 8 fore-aft positions so that there are no turning moments on the ship).

%I A225348 #6 Jun 02 2025 08:33:37
%S A225348 8,77,410,1525,4508,11291,25056,50659,95130,168289,283338,457627,
%T A225348 713374,1078615,1587974,2283803,3217102,4448769,6050622,8106883,
%U A225348 10715232,13988475,18055740,23064277,29180742,36593245,45512628,56174753,68841880
%N A225348 Number of 8Xn -1,1 arrays such that the sum over i=1..8,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 8 fore-aft positions so that there are no turning moments on the ship).
%C A225348 Row 8 of A225345
%H A225348 R. H. Hardin, <a href="/A225348/b225348.txt">Table of n, a(n) for n = 1..210</a>
%F A225348 Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-7) -a(n-8) +a(n-10) +a(n-11) +2*a(n-12) -2*a(n-16) -a(n-17) -a(n-18) +a(n-20) +a(n-21) +a(n-23) -a(n-26) -a(n-27) +a(n-28)
%e A225348 Some solutions for n=4
%e A225348 .-1..1..1..1...-1..1..1..1...-1..1..1..1...-1..1..1..1...-1.-1..1..1
%e A225348 .-1..1..1..1...-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1
%e A225348 .-1.-1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1...-1..1..1..1
%e A225348 .-1.-1.-1.-1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1..1
%e A225348 .-1.-1.-1.-1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1....1..1..1..1
%e A225348 .-1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1.-1..1..1...-1.-1..1..1
%e A225348 .-1.-1.-1..1...-1.-1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1.-1..1
%e A225348 ..1..1..1..1....1..1..1..1...-1.-1.-1.-1....1..1..1..1...-1.-1..1..1
%K A225348 nonn
%O A225348 1,1
%A A225348 _R. H. Hardin_ May 05 2013