

A070925


Number of subsets of A = {1,2,...,n} that have the same center of gravity as A, i.e., (n+1)/2.


1



1, 1, 3, 3, 7, 7, 19, 17, 51, 47, 151, 137, 471, 427, 1519, 1391, 5043, 4651, 17111, 15883, 59007, 55123, 206259, 193723, 729095, 688007, 2601639, 2465133, 9358943, 8899699, 33904323, 32342235, 123580883
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..33.


EXAMPLE

Of the 32 (2^5) sets which can be constructed from the set A = (1,2,3,4,5} only the sets {3}, {2, 3, 4}, {2, 4}, {1, 2, 4, 5}, {1, 2, 3, 4, 5}, {1, 3, 5}, {1, 5} give an average of 3.


MATHEMATICA

Needs["DiscreteMath`Combinatorica`"]; f[n_] := Block[{s = Subsets[n], c = 0, k = 2}, While[k < 2^n + 1, If[ (Plus @@ s[[k]]) / Length[s[[k]]] == (n + 1)/2, c++ ]; k++ ]; c]; Table[ f[n], {n, 1, 20}]


CROSSREFS

Sequence in context: A152113 A146149 A263795 * A146687 A146655 A146812
Adjacent sequences: A070922 A070923 A070924 * A070926 A070927 A070928


KEYWORD

nonn


AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 20 2002


EXTENSIONS

Edited by Robert G. Wilson v and John W. Layman, May 25 2002


STATUS

approved



