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Search: id:A036021
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| A036021 |
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Number of partitions of n into parts not of form 4k+2, 16k, 16k+3 or 16k-3. |
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+0
1
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| 1, 1, 1, 1, 2, 3, 3, 4, 6, 8, 9, 11, 15, 18, 21, 26, 33, 40, 46, 55, 68, 81, 94, 111, 134, 158, 182, 213, 252, 294, 338, 392, 459, 531, 607, 699, 810, 930, 1059, 1212, 1393, 1590, 1804, 2052, 2342, 2660, 3005, 3403, 3862, 4365, 4914, 5540, 6255, 7040, 7899, 8871
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Case k=4,i=2 of Gordon/Goellnitz/Andrews Theorem.
Also number of partitions in which no odd part is repeated, with 1 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.
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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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FORMULA
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Euler transform of period 16 sequence [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, ...]. - Michael Somos, Jul 15 2004
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(1/prod(k=1, n, 1-([1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 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: A071610 A117275 A081230 this_sequence A036025 A036030 A036022
Adjacent sequences: A036018 A036019 A036020 this_sequence A036022 A036023 A036024
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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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