

A050471


a(n) = sum_{dn, n/d=1 mod 4} d^3  sum_{dn, n/d=3 mod 4} d^3.


5



1, 8, 26, 64, 126, 208, 342, 512, 703, 1008, 1330, 1664, 2198, 2736, 3276, 4096, 4914, 5624, 6858, 8064, 8892, 10640, 12166, 13312, 15751, 17584, 18980, 21888, 24390, 26208, 29790, 32768, 34580, 39312, 43092, 44992, 50654, 54864, 57148
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OFFSET

1,2


COMMENTS

Multiplicative because it is the Dirichlet convolution of A000578 = n^3 and A101455 = [1 0 1 0 1 0 1 ...], which are both multiplicative.  Christian G. Bower, May 17 2005


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000
J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 162 (see p. 4 and p. 8).
Index entries for sequences mentioned by Glaisher


FORMULA

G.f.: Sum_{n>=1} n^3*x^n/(1+x^(2*n)).  Vladeta Jovovic, Oct 16 2002


MATHEMATICA

max = 40; s = Sum[n^3*x^(n1)/(1+x^(2*n)), {n, 1, max}] + O[x]^max; CoefficientList[s, x] (* JeanFrançois Alcover, Dec 02 2015, after Vladeta Jovovic *)


PROG

(PARI) a(n) = sumdiv(n, d, d^3*(((n/d) % 4)==1))  sumdiv(n, d, d^3*(((n/d) % 4)==3)); \\ Michel Marcus, Feb 16 2015


CROSSREFS

Cf. A050469, A050470, A050468.
Sequence in context: A002901 A213769 A301647 * A088024 A296112 A051669
Adjacent sequences: A050468 A050469 A050470 * A050472 A050473 A050474


KEYWORD

nonn,mult


AUTHOR

N. J. A. Sloane, Dec 23 1999


EXTENSIONS

Offset changed from 0 to 1 by R. J. Mathar, Jul 15 2010


STATUS

approved



