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A035462
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Number of partitions of n into parts 4k-1.
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2
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1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 2, 4, 4, 3, 4, 5, 5, 5, 6, 7, 8, 7, 8, 11, 10, 10, 13, 14, 14, 15, 17, 19, 20, 20, 24, 27, 26, 28, 33, 35, 35, 39, 44, 46, 48, 52, 58, 62, 63, 69, 78, 80, 83, 93, 100, 104, 111, 120, 130, 137, 143, 156, 169, 175, 185, 203
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,15
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COMMENTS
| Also, number of partitions into parts 8k+3 or 8k+7.
Also number of partitions of n such that 2k-1 and 2k occur with the same multiplicity. Example: a(18)=3 because we have [8,7,2,1],[6,5,4,3] and [2,2,2,2,2,2,1,1,1,1,1,1]. It is easy to find a bijection between these partitions and those described in the definition. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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FORMULA
| G.f.: 1/prod(i>=1, 1-x^(4*i-1)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
G.f.: sum(n>=0, x^(3*n) / prod(k=1..n, 1-x^(4*k) ) ) = 1 + sum(n>=0, x^(4*n+3) / prod(k>=n, 1-x^(4*k+3) ) ) = 1 + sum(n>=0, x^(4*n+3) / prod(k=0..n, 1-x^(4*k+3) ) ). [Joerg Arndt, Apr 8 2011]
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EXAMPLE
| a(18)=3 because we have [15,3],[11,7] and [3,3,3,3,3,3].
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MAPLE
| g:=1/product(1-x^(4*i-1), i=1..50): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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CROSSREFS
| Cf. A035441-A035468.
Sequence in context: A091972 A025833 A200647 * A160735 A120481 A193676
Adjacent sequences: A035459 A035460 A035461 * A035463 A035464 A035465
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Offset changed by N. J. A. Sloane, Apr 11 2010
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