%I A079499
%S A079499 0,1,0,1,2,1,2,1,4,4,4,4,6,7,6,10,12,13,12,16,18,22,22,25,32,36,36,42,
%T A079499 50,53,58,64,76,83,88,99,116,123,132,147,168,181,194,215,240,262,280,
%U A079499 306,346,375,396
%N A079499 Total number of parts in all partitions of n into distinct odd parts.
%C A079499 Also sum of the sizes of the Durfee squares of all self-conjugate partitions 
               of n. Example: a(13)=7 because there are three self-conjugate partitions 
               of 13, namely [7,1,1,1,1,1,1], [5,3,3,1,1] and [4,4,3,2], having 
               Durfee squares of sizes 1,3 and 3, respectively. a(n)=sum(k*A116422(n,
               k),k=1..floor(sqrt(n))). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Feb 14 2006
%D A079499 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (pp. 27-28).
%D A079499 G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge Univ. Press, 
               2004 (pp. 75-78).
%D A079499 A. Knopfmacher and N. Robbins, Identities for the total number of parts 
               in partitions of integers, Util. Math. 67 (2005), 9-18.
%F A079499 G.f.: sum x^(2k-1)/(1+x^(2k-1); k=1..inf * prod (1+x^(2m-1); m=1..inf
%F A079499 Sum_{k>0} (k*x^(k^2)/Product_{j=1..k} (1-x^(2*j))). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Aug 06 2004
%F A079499 G.f.=sum(kx^(k^2)/product(1-x^(2i),i =1..k),k=1..infinity). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Feb 14 2006
%e A079499 a(13)=7 because the partitions of 13 into distinct odd parts are [13], 
               [9,3,1] and [7,5,1] and we have 1+3+3=7 parts.
%p A079499 g:=sum(k*x^(k^2)/product(1-x^(2*i),i =1..k),k=1..20):gser:=series(g,x=0,
               52): seq(coeff(gser,x,n),n=0..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Feb 14 2006
%Y A079499 Cf. A015723, A000700, A067619, A006128.
%Y A079499 Cf. A032021.
%Y A079499 Cf. A116422.
%Y A079499 Sequence in context: A157333 A002852 A099875 this_sequence A166235 A143591 
               A085063
%Y A079499 Adjacent sequences: A079496 A079497 A079498 this_sequence A079500 A079501 
               A079502
%K A079499 nonn
%O A079499 0,5
%A A079499 Arnold Knopfmacher (arnoldk(AT)cam.wits.ac.za), Jan 21 2003