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Search: id:A036017
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| A036017 |
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Number of partitions of n into parts not of form 4k+2, 12k, 12k+1 or 12k-1. |
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+0
1
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| 1, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 6, 7, 10, 12, 13, 15, 19, 23, 26, 29, 36, 44, 48, 54, 66, 77, 86, 98, 115, 134, 150, 169, 197, 227, 253, 285, 329, 375, 418, 470, 536, 607, 678, 757, 858, 969, 1076, 1200, 1353, 1516, 1683, 1873, 2098, 2343, 2596, 2878, 3211
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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Case k=3,i=1 of Gordon/Goellnitz/Andrews Theorem.
Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 2 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even.
Euler transform of period 12 sequence [0,0,1,1,1,0,1,1,1,0,0,0,...]. - Michael Somos Jun 28 2004
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REFERENCES
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G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff(1/prod(k=1, n, 1-([0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0][(k-1)%12+1])*x^k, 1+x*O(x^n)), n))} /* Michael Somos Jun 28 2004 */
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CROSSREFS
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Sequence in context: A108932 A029067 A048460 this_sequence A029066 A035581 A064338
Adjacent sequences: A036014 A036015 A036016 this_sequence A036018 A036019 A036020
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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