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
Keywords
Examples
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
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n = 1..196 from R. H. Hardin)
Programs
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Maple
b:= proc(x, y, t) option remember; `if`(x=0, 1, add(`if`(abs(j)b(n, 0$2): seq(a(n), n=0..33); # Alois P. Heinz, Mar 25 2020
Extensions
a(0)=1 prepended by Alois P. Heinz, Mar 25 2020