Search: id:A089958
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%I A089958
%S A089958 1,0,1,1,1,1,3,1,3,4,4,4,8,5,9,11,11,12,20,15,23,27,28,31,45,38,52,61,
%T A089958 64,71,96,87,112,129,136,151,194,184,227,259,275,304,376,368,441,499,
%U A089958 531,586,704,705,826,927,989,1088,1280,1302,1500,1672,1787,1960,2267
%N A089958 Number of partitions of n in which every part occurs 2, 3, or 5 times.
%C A089958 Also number of partitions of n in which every part is congruent to {2, 
               3, 6, 9, 10} mod 12. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 
               07 2005
%D A089958 M. V. Subbarao, Combinatorial proofs of some identities, Proc. Washington 
               State Univ. Conf. Number Theory, 1971, pp. 80-91.
%D A089958 M. V. Subbarao, On a partition theorem of Mac Mahon-Andrews, Proc. Amer. 
               Math. Soc., 27, 1971, 449-450.
%H A089958 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PartitionFunctionP.html">Partition Function P</a>
%F A089958 Euler transform of period 12 sequence [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 
               0, 0, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2005
%F A089958 Expansion of q^(-5/24)eta(q^6)eta(q^4)/(eta(q^2)eta(q^3)) in powers of 
               q.
%F A089958 G.f.=product(1+x^(2j)+x^(3j)+x^(5j), j=1..infinity). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Mar 05 2006
%e A089958 a(11)=4 because we have [4,4,1,1,1],[3,3,3,1,1],[3,3,1,1,1,1,1] and [2,
               2,2,1,1,1,1,1].
%p A089958 g:=product(1+x^(2*j)+x^(3*j)+x^(5*j),j=1..50): gser:=series(g,x=0,63): 
               seq(coeff(gser,x,n),n=0..60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 05 2006
%o A089958 (PARI) {a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( eta(x^4+A)*eta(x^6+A)/
               eta(x^2+A)/eta(x^3+A), n))} /* Michael Somos Jan 19 2005 */
%Y A089958 Sequence in context: A081772 A050121 A029152 this_sequence A162932 A008924 
               A021323
%Y A089958 Adjacent sequences: A089955 A089956 A089957 this_sequence A089959 A089960 
               A089961
%K A089958 nonn
%O A089958 0,7
%A A089958 Eric Weisstein (eric(AT)weisstein.com), Nov 16, 2003

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