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A025887
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Expansion of 1/((1-x^5)*(1-x^8)*(1-x^9)).
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4
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1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11
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OFFSET
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0,19
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COMMENTS
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a(n) is the number of partitions of n into parts 5, 8, and 9. - Joerg Arndt, Nov 20 2022
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,1,1,0,0,0,-1,-1,0,0,-1,0,0,0,0,1).
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FORMULA
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a(n) = a(n-5) + a(n-8) + a(n-9) - a(n-13) - a(n-14) - a(n-17) + a(n-22). - G. C. Greubel, Nov 19 2022
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MATHEMATICA
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CoefficientList[Series[1/((1-x^5)(1-x^8)(1-x^9)), {x, 0, 80}], x] (* G. C. Greubel, Nov 19 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^8)*(1-x^9)) )); // G. C. Greubel, Nov 19 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^5)*(1-x^8)*(1-x^9)) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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