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}.

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

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, k-1));
thebins(n) = vector(2^n, k, padbin(k-1, 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: A361906 A306829 A067798 * A281704 A350607 A074693

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