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A096981
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Number of partitions of n into parts congruent to {0, 1, 3, 5} mod 6.
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0
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1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 12, 15, 21, 25, 30, 39, 46, 56, 72, 85, 101, 125, 147, 175, 215, 252, 296, 356, 415, 487, 582, 676, 786, 927, 1072, 1244, 1460, 1682, 1939, 2255, 2588, 2976, 3446, 3942, 4510, 5189, 5916, 6751, 7739, 8797, 9999, 11406, 12927, 14657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also, number of partitions of in which the distinct parts are prime to 3 and the unrestricted parts are multiples of 3.
The inverted graded parafermionic partition function. This g.f. is a generalization of A003105, A006950 and A096938
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REFERENCES
| T. M. Apostol, An Introduction to Analytic Number Theory, Springer-Verlag, NY, 1976
Noureddine Chair, Partition identities from partial supersymmetry.
D. Spector, Duality, partial supersymmetry and arithmetic number theory, J. Math. Phys. vol. 39, 1998, p. 1919.
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FORMULA
| Euler transform of period 6 sequence [1, 0, 1, 0, 1, 1, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 20 2004
G.f.: 1/product_{k>=1}(1-x^k+x^(2*k)-x^(3*k)+x^(4*k)-x^(5*k))=Product_{k>=1}(1+X^(3*k-1))(1+x^(3*k-2))/(1-x^(3*k))
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EXAMPLE
| E.g. a(11) = 15 because we can write 11 = 10+1 = 8+2+1 = 7+4 = 5+4+2 (parts do not not contain multiple of 3) = 9+2 = 8+3 = 7+3+1 = 6+5 = 6+4+1 = 6+3+2 = 5+3+3 = 5+3+2+1 = 4+3+3+1 = 3+3+3+2
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MAPLE
| series(product(1/(1-x^k+x^(2*k)-x^(3*k)+x^(4*k)-x^(5*k)), k=1..150), x=0, 100);
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MATHEMATICA
| CoefficientList[ Series[ Product[ 1/(1 - x^k + x^(2k) - x^(3k) + x^(4k) - x^(5k)), {k, 55}], {x, 0, 53}], x] (from Robert G. Wilson v Aug 21 2004)
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CROSSREFS
| Sequence in context: A117752 A172992 A006065 * A035541 A187502 A060966
Adjacent sequences: A096978 A096979 A096980 * A096982 A096983 A096984
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Aug 19 2004
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EXTENSIONS
| Better definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 20 2004
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 21 2004
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