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A129502
For n=2^k, a(n) = binomial(k + 2, 2), else 0.
4
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
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
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