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A029149
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Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)).
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1
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1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 6, 5, 7, 8, 8, 10, 11, 11, 14, 14, 16, 17, 20, 20, 23, 25, 26, 29, 32, 32, 37, 38, 41, 44, 48, 49, 54, 57, 60, 64, 69, 70, 77, 80, 84, 89, 95, 97, 105, 109, 114, 120, 127, 130, 139, 144, 150, 157, 166, 169, 180, 186
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OFFSET
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0,6
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COMMENTS
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a(n) is the number of partitions of n into parts 2, 3, 5, and 12. [Joerg Arndt, Jan 10 2018]
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,-1,-1,0,1,0,1,0,-1,-1,0,0,0,1,1,0,-1).
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FORMULA
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G.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)).
a(n) = a(n-2)+a(n-3)-a(n-7)-a(n-8)+a(n-10)+a(n-12)-a(n-14)-a(n-15)+a(n-19)+a(n-20)-a(n-22). - Wesley Ivan Hurt, May 20 2021
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MATHEMATICA
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CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^12)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, 0, 0, -1, -1, 0, 1, 0, 1, 0, -1, -1, 0, 0, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 6, 5, 7, 8, 8, 10, 11, 11, 14, 14}, 60] (* Harvey P. Dale, Jan 08 2018 *)
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PROG
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(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)))); // Vincenzo Librandi, Jan 10 2018
(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)) + O(x^70)) \\ Jinyuan Wang, Feb 28 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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