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A095941
Number of subsets of {1,2,...,n} such that every number in the set is no larger than the sum of the other numbers in the set.
4
0, 0, 1, 4, 13, 35, 85, 194, 425, 904, 1885, 3878, 7904, 16008, 32282, 64913, 130280, 261145, 523036, 1047017, 2095222, 4191927, 8385695, 16773663, 33550117, 67103645, 134211440, 268427907, 536861880, 1073731053, 2147470842, 4294952115, 8589916646, 17179848025
OFFSET
1,4
COMMENTS
These are the lengths of the sides of a (possibly degenerate) polygon.
Might be called "coalition sets": no member of the set can outnumber all of the others, so a coalition is needed in order to get a majority. - Jaap Spies, Jul 14 2004
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..3321 (first 500 terms from T. D. Noe)
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), j=1..n):
seq(a(n), n=1..37); # Alois P. Heinz, Feb 13 2021
MATHEMATICA
max = 30; -Accumulate[ Accumulate[q = PartitionsQ[ Range[max]]] + 1] + Accumulate[q] + 2^Range[max] - 1 (* Jean-François Alcover, Aug 01 2013, after A095944 *)
CROSSREFS
See A095944 for formula. Cf. A002623.
Sequence in context: A057159 A189588 A266357 * A210843 A177155 A189595
KEYWORD
nonn,nice,easy
AUTHOR
Michael Rieck and W. Edwin Clark, Jul 13 2004
EXTENSIONS
Extended by Alexander D. Healy using data from A095944, Nov 18 2005
STATUS
approved