A225338 - OEIS

A225338

Number of n X 2 -1,1 arrays such that the sum over i=1..n, j=1..2 of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute 2-across galley oarsmen left-right at n fore-aft positions so that there are no turning moments on the ship).

%I #12 Mar 25 2020 18:11:32

%S 1,1,1,1,3,7,15,33,77,181,443,1113,2837,7283,18909,49635,131427,

%T 350419,940417,2538857,6890577,18790165,51462893,141509487,390530601,

%U 1081369087,3003537529,8366306613,23366125605,65420219243,183585473369,516298786843,1454928750641

%N Number of n X 2 -1,1 arrays such that the sum over i=1..n, j=1..2 of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute 2-across galley oarsmen left-right at n fore-aft positions so that there are no turning moments on the ship).

%H Alois P. Heinz, <a href="/A225338/b225338.txt">Table of n, a(n) for n = 0..200</a> (terms n = 1..196 from R. H. Hardin)

%e All solutions for n=4

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

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

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

%p b:= proc(x, y, t) option remember; `if`(x=0, 1, add(`if`(abs(j)

%p <x and abs(y)<x*(x+1)/2, b(x-1, y+j, j), 0), j=t-1..t+1))

%p end:

%p a:= n-> b(n, 0$2):

%p seq(a(n), n=0..33); # _Alois P. Heinz_, Mar 25 2020

%Y Column 2 of A225345.

%Y Cf. A002426.

%K nonn

%O 0,5

%A _R. H. Hardin_, May 05 2013

%E a(0)=1 prepended by _Alois P. Heinz_, Mar 25 2020