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Search: id:A036020
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| A036020 |
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Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 16k-1. |
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+0
1
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| 1, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 7, 8, 11, 14, 15, 18, 23, 28, 32, 36, 45, 55, 61, 70, 86, 101, 114, 131, 155, 182, 206, 234, 275, 319, 359, 408, 474, 544, 612, 694, 797, 909, 1023, 1153, 1315, 1494, 1673, 1881, 2134, 2407, 2693, 3019, 3403, 3825, 4269, 4768
(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=4,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 3 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even.
Euler transform of period 16 sequence [0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,...]. - Michael Somos, Jul 15 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, 1, 1, 1, 0, 0, 0][(k-1)%16+1])*x^k, 1+x*O(x^n)), n))
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CROSSREFS
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Sequence in context: A162157 A060210 A000025 this_sequence A036024 A036029 A035362
Adjacent sequences: A036017 A036018 A036019 this_sequence A036021 A036022 A036023
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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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