cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A092343 #18 Dec 12 2023 05:41:29
%S A092343 9,126,585,1332,3096,4914,9198,12168,19782,24390,37449,43344,61740,
%T A092343 68922,97236,103824,141759,148878,201240,205380,268128,276948,358722,
%U A092343 357912,455886,458208,589806,571788,715572,704970,888264,864360,1061937,1030302,1285830
%N A092343 a(n) = sigma_3(3n+2).
%F A092343 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
%F A092343 Convolution square of A144614. - _Michael Somos_, May 30 2012
%F A092343 Sum_{k=0..n} a(k) ~ (20*zeta(4)/3) * n^4. - _Amiram Eldar_, Dec 12 2023
%e A092343 G.f. = 9 + 126*x + 585*x^2 + 1332*x^3 + 3096*x^4 + 4914*x^5 + 9198*x^6 + 12168*x^7 + ...
%e A092343 G.f. = 9*q^2 + 126*q^5 + 585*q^8 + 1332*q^11 + 3096*q^14 + 4914*q^17 + 9198*q^20 + ...
%t A092343 Table[DivisorSigma[3,3n+2],{n,0,40}] (* _Harvey P. Dale_, Jul 02 2011 *)
%o A092343 (PARI) {a(n) = if( n<0, 0, sigma( 3*n + 2, 3))}; /* _Michael Somos_, May 30 2012 */
%Y A092343 Trisection of A001158.
%Y A092343 Cf. A013662, A045823, A091986, A092341, A092342, A144614.
%K A092343 nonn,easy
%O A092343 0,1
%A A092343 _N. J. A. Sloane_, Mar 20 2004