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Search: id:A097451
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| A097451 |
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Number of partitions of n into parts congruent to {2, 3, 4} mod 6. |
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+0
1
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| 1, 0, 1, 1, 2, 1, 3, 2, 5, 4, 7, 6, 11, 9, 15, 14, 22, 20, 31, 29, 43, 41, 58, 57, 80, 78, 106, 107, 142, 143, 188, 191, 247, 253, 321, 332, 418, 432, 537, 561, 690, 721, 880, 924, 1118, 1178, 1412, 1493, 1781, 1884, 2231, 2370, 2789, 2965, 3472, 3698, 4309, 4596
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of partitions of n in which no part is 1, no part appears more than twice and no two parts differ by 1. Example: a(6)=3 because we have [6],[4,2] and [3,3]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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REFERENCES
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G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, Exercise 7.9.
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FORMULA
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Euler transform of period 6 sequence [0, 1, 1, 1, 0, 0, ...].
G.f.=1/product((1-x^(2+6j))(1-x^(3+6j))(1-x^(4+6j)), j=0..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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EXAMPLE
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a(8)=5 because we have [8],[44],[422],[332] and [2222].
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MAPLE
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g:=1/product((1-x^(2+6*j))*(1-x^(3+6*j))*(1-x^(4+6*j)), j=0..15): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=0..67); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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CROSSREFS
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Cf. A070047.
Sequence in context: A053602 A123231 A058736 this_sequence A005916 A034392 A034393
Adjacent sequences: A097448 A097449 A097450 this_sequence A097452 A097453 A097454
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 23 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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