cp's OEIS Frontend

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 A225338 #12 Mar 25 2020 18:11:32
%S A225338 1,1,1,1,3,7,15,33,77,181,443,1113,2837,7283,18909,49635,131427,
%T A225338 350419,940417,2538857,6890577,18790165,51462893,141509487,390530601,
%U A225338 1081369087,3003537529,8366306613,23366125605,65420219243,183585473369,516298786843,1454928750641
%N 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).
%H A225338 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 A225338 All solutions for n=4
%e A225338 .-1..1...-1.-1....1..1
%e A225338 .-1..1....1..1...-1.-1
%e A225338 .-1..1....1..1...-1.-1
%e A225338 .-1..1...-1.-1....1..1
%p A225338 b:= proc(x, y, t) option remember; `if`(x=0, 1, add(`if`(abs(j)
%p A225338       <x and abs(y)<x*(x+1)/2, b(x-1, y+j, j), 0), j=t-1..t+1))
%p A225338     end:
%p A225338 a:= n-> b(n, 0$2):
%p A225338 seq(a(n), n=0..33);  # _Alois P. Heinz_, Mar 25 2020
%Y A225338 Column 2 of A225345.
%Y A225338 Cf. A002426.
%K A225338 nonn
%O A225338 0,5
%A A225338 _R. H. Hardin_, May 05 2013
%E A225338 a(0)=1 prepended by _Alois P. Heinz_, Mar 25 2020