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).

1, 1, 1, 1, 3, 7, 15, 33, 77, 181, 443, 1113, 2837, 7283, 18909, 49635, 131427, 350419, 940417, 2538857, 6890577, 18790165, 51462893, 141509487, 390530601, 1081369087, 3003537529, 8366306613, 23366125605, 65420219243, 183585473369, 516298786843, 1454928750641

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n = 1..196 from R. H. Hardin)

Example

All solutions for n=4
.-1..1...-1.-1....1..1
.-1..1....1..1...-1.-1
.-1..1....1..1...-1.-1
.-1..1...-1.-1....1..1

Maple

b:= proc(x, y, t) option remember; `if`(x=0, 1, add(`if`(abs(j)
      <x and abs(y)<x*(x+1)/2, b(x-1, y+j, j), 0), j=t-1..t+1))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..33);  # Alois P. Heinz, Mar 25 2020

Crossrefs

Column 2 of A225345.

Cf. A002426.

Sequence in context: A249512 A140498 A136029 * A101892 A211279 A351660

Adjacent sequences: A225335 A225336 A225337 * A225339 A225340 A225341

Keyword

nonn

Author

R. H. Hardin, May 05 2013

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 25 2020

Status

approved