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Search: id:A070048
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| A070048 |
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Number of partitions of n into odd parts in which no part appears more than thrice. |
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+0
3
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| 1, 1, 1, 2, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 11, 13, 16, 18, 21, 24, 27, 32, 36, 41, 48, 54, 61, 70, 78, 88, 100, 112, 127, 143, 159, 179, 199, 222, 248, 276, 308, 342, 380, 421, 465, 516, 570, 629, 697, 767, 845, 932, 1022, 1124, 1236, 1355, 1488, 1631, 1785, 1954, 2136
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also number of partitions of n into distinct parts in which no part is multiple of 4. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 31 2004
McKay-Thompson series of class 64a for the Monster group.
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REFERENCES
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G. E. Andrews, An algebraic identity of F. H. Jackson ..., Discrete Math., 232 (2001), 77-83.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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G.f.: Product_{i>0} (1+x^i)/(1+x^(4*i)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 31 2004
Expansion of q^(1/8)eta(q^2)eta(q^4)/(eta(q)eta(q^8)) in powers of q.
Euler transform of period 8 sequence [1, 0, 1, -1, 1, 0, 1, 0, ...].
G.f.: Product_{k>0} (1-x^(8k-4))/(1-x^(2k-1)).
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EXAMPLE
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T64a = 1/q + q^7 + q^15 + 2q^23 + q^31 + 2q^39 + 3q^47 + 3q^55 +...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^4+A)/ eta(x+A)/ eta(x^8+A), n))}
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CROSSREFS
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Sequence in context: A087188 A102885 A138585 this_sequence A116498 A143472 A015739
Adjacent sequences: A070045 A070046 A070047 this_sequence A070049 A070050 A070051
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 09 2002
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EXTENSIONS
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Additional comments from Michael Somos, Dec 04 2002
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