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Search: id:A036026
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| A036026 |
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Number of partitions of n into parts not of forms 4*k+2, 20*k, 20*k+5 or 20*k+15. |
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+0
5
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| 1, 1, 1, 2, 3, 3, 4, 6, 8, 10, 12, 16, 21, 25, 30, 38, 48, 57, 68, 84, 102, 121, 143, 172, 207, 243, 284, 338, 400, 465, 542, 636, 744, 862, 996, 1158, 1344, 1546, 1776, 2050, 2361, 2701, 3088, 3540, 4050, 4613, 5248, 5980, 6808, 7719, 8742, 9916, 11232
(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=5,i=3 of Gordon/Goellnitz/Andrews Theorem.
Number of partitions in which no odd part is repeated, with at most 2 parts of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smaller part is odd and greater than 2 when the smaller 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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Expansion of psi(-q^5) / psi(-q) in powers of q where psi() is a Ramanujan theta function. - Michael Somos Oct 27 2008
Expansion of q^(-1/2) * eta(q^2) * eta(q^5) * eta(q^20) / (eta(q) * eta(q^4) * eta(q^10)) in powers of q. - Michael Somos Oct 27 2008
Euler transform of period 20 sequence [ 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, ...]. - Michael Somos Oct 27 2008
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EXAMPLE
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q + q^3 + q^5 + 2*q^7 + 3*q^9 + 3*q^11 + 4*q^13 + 6*q^15 + 8*q^17 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^10 + A)), n))} /* Michael Somos Oct 27 2008 */
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CROSSREFS
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A145722(n) = a(2*n). A101277(n) = a(2*n + 1). Convolution inverse of A145708.
Sequence in context: A036025 A036030 A036022 this_sequence A116494 A036031 A017818
Adjacent sequences: A036023 A036024 A036025 this_sequence A036027 A036028 A036029
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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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