

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.


3



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
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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

T. D. Noe, Table of n, a(n) for n=1..500


MATHEMATICA

max = 30; Accumulate[ Accumulate[q = PartitionsQ[ Range[max]]] + 1] + Accumulate[q] + 2^Range[max]  1 (* JeanFrançois Alcover, Aug 01 2013, after A095944 *)


CROSSREFS

See A095944 for formula. Cf. A002623.
Sequence in context: A057159 A189588 A266357 * A210843 A177155 A189595
Adjacent sequences: A095938 A095939 A095940 * A095942 A095943 A095944


KEYWORD

nonn,nice,easy


AUTHOR

Michael Rieck and W. Edwin Clark, Jul 13 2004


EXTENSIONS

Extended by Alex Healy using data from A095944, Nov 18 2005


STATUS

approved



