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A225346 Number of 6Xn -1,1 arrays such that the sum over i=1..6,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 6 fore-aft positions so that there are no turning moments on the ship).

%I A225346 #6 Jun 02 2025 08:33:24
%S A225346 0,15,0,107,0,397,0,1081,0,2399,0,4675,0,8273,0,13641,0,21267,0,31731,
%T A225346 0,45637,0,63697,0,86635,0,115291,0,150513,0,193269,0,244527,0,305383,
%U A225346 0,376929,0,460389,0,556975,0,668043,0,794921,0,939097,0,1102023,0,1285311
%N A225346 Number of 6Xn -1,1 arrays such that the sum over i=1..6,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 6 fore-aft positions so that there are no turning moments on the ship).
%C A225346 Row 6 of A225345
%H A225346 R. H. Hardin, <a href="/A225346/b225346.txt">Table of n, a(n) for n = 1..210</a>
%F A225346 Empirical: a(n) = a(n-2) +2*a(n-4) -a(n-6) -2*a(n-8) +a(n-12) -a(n-14) +2*a(n-18) +a(n-20) -2*a(n-22) -a(n-24) +a(n-26)
%e A225346 Some solutions for n=4
%e A225346 .-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1..1..1...-1..1..1..1
%e A225346 .-1.-1.-1..1...-1..1..1..1....1..1..1..1...-1.-1..1..1...-1.-1.-1.-1
%e A225346 .-1.-1.-1..1....1..1..1..1...-1.-1.-1..1....1..1..1..1...-1.-1.-1..1
%e A225346 ..1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1....1..1..1..1
%e A225346 .-1.-1.-1.-1....1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1
%e A225346 .-1..1..1..1...-1.-1.-1.-1....1..1..1..1....1..1..1..1...-1.-1.-1.-1
%K A225346 nonn
%O A225346 1,2
%A A225346 _R. H. Hardin_ May 05 2013