OFFSET
0,5
COMMENTS
In other words, every element of S is strictly less than half the sum.
LINKS
math.stackexchange, Permutation and Combinatorics Problem
FORMULA
EXAMPLE
For n = 5 the a(5)=9 subsets are {2,3,4}, {2,4,5}, {3,4,5}, {1,2,3,4}, {1,2,3,5}, {1,2,4,5}, {1,3,4,5}, {2,3,4,5}, and {1,2,3,4,5}.
MAPLE
b:= proc(n, s) option remember; `if`(s<1, 2^n,
`if`(n*(n+1)/2<s, 0, b(n-1, s)+b(n-1, max(0, s-n))))
end:
a:= n-> add(b(j-1, j+1), j=1..n):
seq(a(n), n=0..37); # Alois P. Heinz, Feb 13 2021
MATHEMATICA
gf := (1 - x - x^2)/((1 - 2 x) (1 - x)^2) - QPochhammer[-1, x]/(2 (1 - x)^2);
CoefficientList[Series[gf, {x, 0, 34}], x] (* Peter Luschny, Feb 13 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Feb 13 2021
STATUS
approved