|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(2^e) = binomial(e + 2, 2), a(p^e) = 0 for odd prime p.
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
|
|
|
EXTENSIONS
|
Name changed and terms a(40) and beyond from Andrew Howroyd, Aug 03 2018
|
|
STATUS
|
approved
|
|
|
|