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Search: id:A036023
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| A036023 |
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Number of partitions of n into parts not of form 4k+2, 16k, 16k+7 or 16k-7. |
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1
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| 1, 1, 1, 2, 3, 4, 5, 6, 9, 11, 13, 17, 22, 27, 32, 40, 50, 60, 71, 86, 105, 125, 146, 174, 209, 245, 285, 336, 396, 461, 534, 621, 725, 838, 963, 1113, 1287, 1477, 1689, 1938, 2224, 2538, 2888, 3293, 3755, 4265, 4830, 5478, 6215, 7024, 7923, 8947, 10098
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Case k=4,i=4 of Gordon/Goellnitz/Andrews Theorem.
Also number of partitions in which no odd part is repeated, with at most 3 parts 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 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,0,...]. - 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-([1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 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: A108957 A080112 A123924 this_sequence A119952 A102571 A064278
Adjacent sequences: A036020 A036021 A036022 this_sequence A036024 A036025 A036026
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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