login
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).
2
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 05 2013
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Mar 25 2020
STATUS
approved