

A205536


Number of distinct values of Sum_{i=0..n} x(i)*binomial(n,i), where the x(i) is a vector of length n+1 that runs through all combinations of {0, 1}.


5



2, 3, 5, 9, 15, 21, 45, 57, 117, 243, 395, 465, 879, 1053, 2039, 5949, 10325, 11739, 21345, 22005, 64917, 132167, 187681, 252531, 775059, 1215147, 2126091, 3883077, 6003423, 8207583, 19058065, 21162879, 46406677, 70113033, 100115753, 280588533, 699418771, 838568259
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OFFSET

0,1


LINKS

Table of n, a(n) for n=0..37.


MATHEMATICA

a[n_] := Length @ Union[Total /@ Subsets[Table[Binomial[n, k], {k, 0, n}]]]; Array[a, 10, 0] (* Amiram Eldar, Jan 11 2019 *)


PROG

(PARI) padbin(k, n) = my(p = Pol(binary(k))); vector(n, k, polcoeff(p, k1));
thebins(n) = vector(2^n, k, padbin(k1, n));
a(n) = my(vv = thebins(n+1)); #Set(vector(#vv, k, sum(i=0, n, vv[k][i+1]*binomial(n, i)))); \\ Michel Marcus, Jan 11 2019


CROSSREFS

Cf. A007318, A205537, A205538, A205539, A205540, A205541.
Column 1 of A205542.
Sequence in context: A085897 A306829 A067798 * A281704 A074693 A147322
Adjacent sequences: A205533 A205534 A205535 * A205537 A205538 A205539


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 28 2012


EXTENSIONS

Value range in title corrected and a(29)a(31) added by Aaron Meyerowitz, Jun 13 2014
a(32)a(37) from Bert Dobbelaere, Sep 15 2019


STATUS

approved



