Search: id:A003105
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%I A003105 M0254
%S A003105 1,1,1,1,1,2,2,3,3,3,4,5,6,7,8,9,10,12,14,16,18,20,23,26,30,34,38,42,47,
%T A003105 53,60,67,74,82,91,102,114,126,139,153,169,187,207,228,250,274,301,331,
%U A003105 364,399,436,476,520,569,622,679,739,804,875,953,1038,1128,1224,1327
%N A003105 Number of partitions of n into parts 6n+1 or 6n-1.
%C A003105 McKay-Thompson series of class 72e for the Monster group.
%C A003105 Also number of partitions of n into odd parts in which no part appears 
               more than twice, cf. A070048 and A096938. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jan 18 2005
%C A003105 Also number of partitions of n into distinct parts congruent to 1 or 
               2 modulo 3. (Follows from second G.F.) - Naoki Sato (nsato7(AT)yahoo.ca), 
               Jul 20 2005
%D A003105 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003105 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%H A003105 R. Zumkeller, <a href="b003105.txt">Table of n, a(n) for n = 0..200</
               a>
%H A003105 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A003105 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SchursPartitionTheorem.html">Link to a section of The World of Mathematics.</
               a>
%H A003105 N. Chair, <a href="http://arXiv.org/abs/hep-th/0409011">Partition identities 
               from Partial Supersymmetry</a>
%F A003105 G.f.: 1/Product_{k>=0} (1-x^(6*k+1))*(1-x^(6*k+5)) = Product_{k>=0} (1+x^(3*k+1))*(1+x^(3*k+2)) 
               = 1/Product_{k>=0} (1-x^k+x^(2*k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jun 08 2003
%F A003105 Expansion of q^(1/12)eta(q^2)eta(q^3)/(eta(q)eta(q^6)) in powers of q.
%F A003105 Euler transform of period 6 sequence [1, 0, 0, 0, 1, 0, ...]. - Michael 
               Somos, Jan 09 2005
%F A003105 Given g.f. A(x), then B(x)=(A(x^12)/x)^4 satisfies 0=f(B(x), B(x^2)) 
               where f(u, v)=uv^4+(1-u^3)v^3+6u^2v^2+(u^4-u)v+u^3 - Michael Somos, 
               Jan 09 2005
%e A003105 T72e = 1/q + q^11 + q^23 + q^35 + q^47 + 2q^59 + 2q^71 + 3q^83 + ...
%o A003105 (PARI) {a(n)=local(A); if(n<0,0,A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)/
               eta(x+A)/eta(x^6+A),n))} /* Michael Somos Jan 09 2005 */
%Y A003105 Cf. A001651, A000726, A132462, A132463.
%Y A003105 Sequence in context: A125059 A029112 A029094 this_sequence A081166 A036846 
               A058740
%Y A003105 Adjacent sequences: A003102 A003103 A003104 this_sequence A003106 A003107 
               A003108
%K A003105 nonn
%O A003105 0,6
%A A003105 N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson
%E A003105 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 08 2003

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