A133179 - OEIS

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

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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, 2;

1, 3;

1, 4, 6;

1, 5, 10 ;...

A034868 modulo 2:

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