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A001343 Number of (unordered) ways of making change for n cents using coins of 5, 10, 20, 50, 100 cents. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Number of partitions of n into parts 5, 10, 20, 50, and 100. - Joerg Arndt, Sep 05 2014

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 185

Index entries for linear recurrences with constant coefficients, order 185.

Index entries for sequences related to making change.

FORMULA

G.f.: 1/((1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)*(1-x^100)).

MAPLE

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);

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A254612 A227189 A234859 * A022882 A171919 A000089

Adjacent sequences:  A001340 A001341 A001342 * A001344 A001345 A001346

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified November 21 09:48 EST 2018. Contains 317446 sequences. (Running on oeis4.)