A133179 A modular binomial sum transform of 2^n .

1, 1, 1, 3, 1, 3, 5, 15, 1, 3, 5, 15, 17, 51, 85, 255, 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

a(n) = Sum_{k=0..floor(n/2)} mod(binomial(n,k),2) * 2^k.

Example

A034868 is:
1;
1;
1, 2;
1, 3;
1, 4, 6;
1, 5, 10 ;...
A034868 modulo 2:
1;
1;
1, 0;
1, 1;
1, 0, 0;
1, 1, 0 ;...
a(0)=1*2^0 = 1;
a(1)=1*2^0 = 1;
a(2)=1*2^0+0*2^1 = 1;
a(3)=1*2^0+1*2^1 = 3;
a(4)=1*2^0+0*2^1+0*2^2 = 1
a(5)=1*2^0+1*2^1+0*2^2 = 3

Mathematica

A133179[n_] := Sum[2^k*Mod[Binomial[n, k], 2], {k, 0, Floor[n/2]}]; Table[A133179[n], {n, 0, 50}] (* G. C. Greubel, Aug 11 2017 *)

Crossrefs

Cf. A034868, A048896, A101692, A130047.

Sequence in context: A050820 A261869 A279697 * A282221 A146908 A279249

Adjacent sequences: A133176 A133177 A133178 * A133180 A133181 A133182

Keyword

nonn,tabf

Author

Philippe Deléham, Oct 10 2007

Status

approved