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

Author

Gary W. Adamson, Apr 17 2007

Keywords

• nonn
• easy
• mult

Comments

Row sums of triangle A129501.

Examples

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

Links

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

Crossrefs

Row sums of A129501.

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

Programs

Mathematica

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

PARI

a(n)={my(e=valuation(n, 2)); if(n==1<Andrew Howroyd, Aug 03 2018

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

Extensions

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