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Search: id:A122580
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| A122580 |
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Number of partitions of n with crank congruent to 0 mod 3, minus number of partitions of n with crank congruent to 1 mod 3. |
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+0
1
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| 1, -2, -1, 3, -1, 1, 2, -3, -2, 3, -3, -1, 5, -4, 0, 5, -3, 0, 7, -8, -3, 9, -6, -2, 9, -10, -3, 13, -11, -1, 15, -13, -3, 18, -14, -3, 22, -20, -7, 27, -21, -3, 29, -27, -8, 34, -30, -7, 42, -37, -8, 48, -39, -9, 55, -50, -13, 66, -52, -11, 74
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For a partition p, let l(p) = largest part of p, w(p) = number of 1's in p, m(p) = number of parts of p larger than w(p). The crank of p is given by l(p) if w(p) = 0, otherwise m(p)-w(p).
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LINKS
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Daniel M. Kane, RESOLUTION OF A CONJECTURE OF ANDREWS AND LEWIS INVOLVING CRANKS OF PARTITIONS
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FORMULA
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G.f.: Product((1-x^n)/(1+x^n+x^(2*n)),n=1..infinity). Euler transform of period 3 sequence [ -2,-2,-1, ...].
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CROSSREFS
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Sequence in context: A138618 A140583 A123507 this_sequence A107041 A070099 A126760
Adjacent sequences: A122577 A122578 A122579 this_sequence A122581 A122582 A122583
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KEYWORD
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easy,sign
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 20 2006
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