A225350 - OEIS

%I #6 May 07 2013 07:01:12

%S 0,443,0,24893,0,360909,0,2676331,0,13280209,0,50435657,0,158259755,0,

%T 430394067,0,1047240813,0,2331232209,0,4825180007,0,9399464741,0,

%U 17394354077,0,30804515135,0,52513235123,0,86584738985,0,138623327831,0

%N Number of 10Xn -1,1 arrays such that the sum over i=1..10,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 10 fore-aft positions so that there are no turning moments on the ship)

%C Row 10 of A225345

%H R. H. Hardin, <a href="/A225350/b225350.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-2) +a(n-4) -a(n-10) -a(n-14) -a(n-20) +2*a(n-24) +a(n-26) +a(n-28) +a(n-30) -a(n-34) -a(n-36) -a(n-38) -2*a(n-40) -a(n-42) -a(n-44) +a(n-46) +a(n-48) +2*a(n-50) +a(n-52) +a(n-54) +a(n-56) -a(n-60) -a(n-62) -a(n-64) -2*a(n-66) +a(n-70) +a(n-76) +a(n-80) -a(n-86) -a(n-88) +a(n-90)

%e Some solutions for n=4

%e ..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1

%e .-1.-1.-1.-1....1..1..1..1...-1..1..1..1...-1..1..1..1...-1..1..1..1

%e .-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1

%e .-1..1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1....1..1..1..1

%e ..1..1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1

%e .-1.-1.-1.-1...-1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1.-1

%e .-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1

%e .-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1....1..1..1..1

%e ..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1..1..1

%e .-1.-1..1..1....1..1..1..1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1

%K nonn

%O 1,2

%A _R. H. Hardin_ May 05 2013