A092343 a(n) = sigma_3(3n+2).

9, 126, 585, 1332, 3096, 4914, 9198, 12168, 19782, 24390, 37449, 43344, 61740, 68922, 97236, 103824, 141759, 148878, 201240, 205380, 268128, 276948, 358722, 357912, 455886, 458208, 589806, 571788, 715572, 704970, 888264, 864360, 1061937, 1030302, 1285830

Offset

0,1

Links

Table of n, a(n) for n=0..34.

Formula

Expansion of q^(-2/3) * (a(q) * c(q))^2 in powers of q where a(), c() are cubic AGM theta functions. - Michael Somos, May 30 2012

Convolution square of A144614. - Michael Somos, May 30 2012

Sum_{k=0..n} a(k) ~ (20*zeta(4)/3) * n^4. - Amiram Eldar, Dec 12 2023

Example

G.f. = 9 + 126*x + 585*x^2 + 1332*x^3 + 3096*x^4 + 4914*x^5 + 9198*x^6 + 12168*x^7 + ...
G.f. = 9*q^2 + 126*q^5 + 585*q^8 + 1332*q^11 + 3096*q^14 + 4914*q^17 + 9198*q^20 + ...

Mathematica

Table[DivisorSigma[3, 3n+2], {n, 0, 40}] (* Harvey P. Dale, Jul 02 2011 *)

Prog

(PARI) {a(n) = if( n<0, 0, sigma( 3*n + 2, 3))}; /* Michael Somos, May 30 2012 */

Crossrefs

Trisection of A001158.

Cf. A013662, A045823, A091986, A092341, A092342, A144614.

Sequence in context: A324201 A224495 A064199 * A261176 A261743 A229283

Adjacent sequences: A092340 A092341 A092342 * A092344 A092345 A092346

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 20 2004

Status

approved