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A225352 Number of 12Xn -1,1 arrays such that the sum over i=1..12,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 12 fore-aft positions so that there are no turning moments on the ship).

%I A225352 #8 Jun 02 2025 08:34:05
%S A225352 58,2837,47990,437763,2680534,12439855,47084448,152452967,436320984,
%T A225352 1129965973,2694285574,5993361143,12566218452,25037146431,47716202440,
%U A225352 87454967053,154837885246,265807450011,443841357932,722822838305
%N A225352 Number of 12Xn -1,1 arrays such that the sum over i=1..12,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 12 fore-aft positions so that there are no turning moments on the ship).
%C A225352 Row 12 of A225345
%H A225352 R. H. Hardin, <a href="/A225352/b225352.txt">Table of n, a(n) for n = 1..210</a>
%F A225352 Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-7) +a(n-14) +2*a(n-15) +a(n-16) -a(n-19) -a(n-20) -a(n-21) -2*a(n-22) -a(n-23) -a(n-24) -a(n-26) +2*a(n-27) +2*a(n-28) +2*a(n-29) +2*a(n-30) +a(n-31) +a(n-32) -a(n-34) -a(n-35) -2*a(n-36) -2*a(n-37) -2*a(n-38) -2*a(n-39) +a(n-40) +a(n-42) +a(n-43) +2*a(n-44) +a(n-45) +a(n-46) +a(n-47) -a(n-50) -2*a(n-51) -a(n-52) +a(n-59) +a(n-61) -a(n-64) -a(n-65) +a(n-66)
%e A225352 Some solutions for n=4
%e A225352 .-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1..1
%e A225352 .-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1...-1..1..1..1...-1.-1.-1.-1
%e A225352 .-1.-1..1..1...-1..1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1
%e A225352 .-1..1..1..1....1..1..1..1...-1..1..1..1....1..1..1..1...-1..1..1..1
%e A225352 ..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1
%e A225352 .-1..1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1
%e A225352 .-1.-1..1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1.-1..1..1....1..1..1..1
%e A225352 .-1.-1.-1..1....1..1..1..1...-1.-1..1..1....1..1..1..1...-1..1..1..1
%e A225352 .-1.-1.-1.-1...-1.-1.-1..1....1..1..1..1...-1.-1.-1.-1....1..1..1..1
%e A225352 ..1..1..1..1...-1..1..1..1...-1.-1.-1.-1...-1..1..1..1...-1..1..1..1
%e A225352 .-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1
%e A225352 .-1.-1..1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1.-1
%K A225352 nonn
%O A225352 1,1
%A A225352 _R. H. Hardin_ May 05 2013