A129502 For n=2^k, a(n) = binomial(k + 2, 2), else 0.

1, 3, 0, 6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

Row sums of triangle A129501.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1024

Formula

From Andrew Howroyd, Aug 04 2018: (Start)

Multiplicative with a(2^e) = binomial(e + 2, 2), a(p^e) = 0 for odd prime p.

Dirichlet convolution of A104117 and A209229.

a(n) = Sum_{d|n} A104117(n/d) * A209229(d). (End)

Dirichlet g.f.: 1/(1 - 1/2^s)^3. - Amiram Eldar, Oct 28 2023

Example

a(4) = 6 = sum of A129501 terms: (3 + 2 + 0 + 1).

Mathematica

Table[If[IntegerQ[Log2[n]], Binomial[Log2[n]+2, 2], 0], {n, 100}] (* Harvey P. Dale, May 10 2022 *)

Prog

(PARI) a(n)={my(e=valuation(n, 2)); if(n==1<<e, binomial(2+e, 2), 0)} \\ Andrew Howroyd, Aug 03 2018

Crossrefs

Row sums of A129501.

Cf. A209229, A104117, A129360, A115361, A103994, A000217, A317673.

Sequence in context: A088969 A009780 A175677 * A099892 A060147 A268142

Adjacent sequences: A129499 A129500 A129501 * A129503 A129504 A129505

Keyword

nonn,easy,mult

Author

Gary W. Adamson, Apr 17 2007

Extensions

Name changed and terms a(40) and beyond from Andrew Howroyd, Aug 03 2018

Status

approved