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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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
| N. J. A. Sloane, Transforms
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FORMULA
| EULER transform of A046951.
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EXAMPLE
| 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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PROG
| (PARI) N=66; x='x+O('x^N); gf=1/prod(j=1, N, eta(x^(j^2))); Vec(gf) /* Joerg Arndt, May 03 2008 */
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CROSSREFS
| Cf. A038538.
Sequence in context: A022943 A068491 A024788 * A003405 A153918 A114319
Adjacent sequences: A004098 A004099 A004100 * A004102 A004103 A004104
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, formula and better description from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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