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A225347 Number of 7Xn -1,1 arrays such that the sum over i=1..7,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 7 fore-aft positions so that there are no turning moments on the ship).

%I A225347 #6 Jun 02 2025 08:33:31
%S A225347 0,33,0,395,0,2073,0,7261,0,19709,0,45385,0,92673,0,173189,0,301799,0,
%T A225347 497661,0,783969,0,1189311,0,1747059,0,2497109,0,3484867,0,4763439,0,
%U A225347 6392095,0,8439027,0,10979255,0,14097919,0,17887629,0,22452391,0
%N A225347 Number of 7Xn -1,1 arrays such that the sum over i=1..7,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 7 fore-aft positions so that there are no turning moments on the ship).
%C A225347 Row 7 of A225345
%H A225347 R. H. Hardin, <a href="/A225347/b225347.txt">Table of n, a(n) for n = 1..210</a>
%F A225347 Empirical: a(n) = a(n-2) +a(n-4) -a(n-10) -2*a(n-14) +a(n-18) +a(n-20) +a(n-22) +a(n-24) -2*a(n-28) -a(n-32) +a(n-38) +a(n-40) -a(n-42)
%e A225347 Some solutions for n=4
%e A225347 .-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1.-1...-1.-1..1..1
%e A225347 .-1.-1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1.-1
%e A225347 .-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1
%e A225347 .-1..1..1..1...-1.-1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
%e A225347 .-1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1.-1.-1..1
%e A225347 .-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1..1..1..1....1..1..1..1
%e A225347 .-1.-1..1..1....1..1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1
%K A225347 nonn
%O A225347 1,2
%A A225347 _R. H. Hardin_ May 05 2013