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Search: id:A004101
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| A004101 |
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Number of partitions of n of the form a_1*b_1^2 + a_2*b_2^2 + ...
(Formerly M0753)
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+0
4
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| 1, 1, 2, 3, 6, 8, 13, 18, 29, 40, 58, 79, 115, 154, 213, 284, 391, 514, 690, 900, 1197, 1549, 2025, 2600, 3377, 4306, 5523, 7000, 8922, 11235, 14196, 17777, 22336, 27825, 34720, 43037, 53446, 65942, 81423, 100033, 122991, 150481, 184149
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. Knopfmacher, Abstract Analytic Number Theory. North-Holland, Amsterdam, 1975, p. 293.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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EULER transform of A046951.
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EXAMPLE
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4 = 4*1^2 = 1*2^2 = 3*1^2 + 1*1^2 = 2*1^2 + 2*1^2 = 2*1^2 + 1*1^2 + 1*1^2 = 1*1^2 + 1*1^2 + 1*1^2 + 1*1^2.
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PROGRAM
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(PARI) 1/prod(j=1, N, eta(x^(j^2))); Vec(%) - Joerg Arndt (arndt(AT)jjj.de), May 03 2008
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CROSSREFS
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Cf. A038538.
Sequence in context: A022943 A068491 A024788 this_sequence A003405 A153918 A114319
Adjacent sequences: A004098 A004099 A004100 this_sequence A004102 A004103 A004104
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, formula and better description from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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