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A001343
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Number of (unordered) ways of making change for n cents using coins of 5, 10, 20, 50, 100 cents.
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2
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1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 13, 0, 0, 0, 0, 13, 0, 0, 0, 0, 18, 0, 0, 0, 0, 18, 0, 0, 0, 0, 24, 0, 0, 0, 0, 24, 0, 0, 0, 0, 31, 0, 0, 0, 0
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OFFSET
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0,11
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COMMENTS
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Number of partitions of n into parts 5, 10, 20, 50, and 100. - Joerg Arndt, Sep 05 2014
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.
G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.
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LINKS
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FORMULA
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G.f.: 1/((1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)*(1-x^100)).
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MAPLE
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1/(1-x^5)/(1-x^10)/(1-x^20)/(1-x^50)/(1-x^100): seq(coeff(series(%, x, n+1), x, n), n=0..80);
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MATHEMATICA
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nn = 100; CoefficientList[Series[1/((1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50) (1 - x^100)), {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)
Table[Length[FrobeniusSolve[{5, 10, 20, 50, 100}, n]], {n, 0, 80}] (* very slow, Harvey P. Dale, May 19 2012 *)
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PROG
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(PARI) a(n)=(n%5<1)*floor(((n\10)^4+38*(n\10)^3+476*(n\10)^2+2185*(n\10)+3734)/2400+(n\10+1)*(-1)^(n\10)/160+(n\10\5+1)*[0, 0, 1, 0, -1][n\10%5+1]/10) \\ Tani Akinari, May 14 2014
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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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