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A169718 Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 and 100 cents. 6
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 13, 13, 13, 13, 13, 18, 18, 18, 18, 18, 24, 24, 24, 24, 24, 31, 31, 31, 31, 31, 39, 39, 39, 39, 39, 50, 50, 50, 50, 50, 62, 62, 62, 62, 62, 77, 77, 77, 77, 77, 93, 93, 93, 93, 93, 112, 112, 112, 112, 112, 134, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) = A001300(n) for n < 100; a(n) = A001299(n) for n < 50. - Reinhard Zumkeller, Dec 15 2013

Number of partitions of n into parts 1, 5, 10, 25, 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..10000

M. Erickson, Change for a dollar, change for a million, Math. Horizons, Feb 2010, pp. 22-25.

Index entries for sequences related to making change.

Index entries for linear recurrences with constant coefficients, order 191.

FORMULA

G.f.: 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)*(1-x^100)).

MATHEMATICA

Table[Length[FrobeniusSolve[{1, 5, 10, 25, 50, 100}, n]], {n, 0, 80}] (* or *) CoefficientList[Series[1/((1-x)(1-x^5)(1-x^10)(1-x^25)(1-x^50)(1-x^100)), {x, 0, 80}], x] (* Harvey P. Dale, Dec 25 2011 *)

PROG

(Haskell)

a169718 = p [1, 5, 10, 25, 50, 100] where

   p _          0 = 1

   p []         _ = 0

   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

-- Reinhard Zumkeller, Dec 15 2013

CROSSREFS

Cf. A001299, A001300, A000008.

Sequence in context: A187243 A001299 A001300 * A001306 A260984 A108105

Adjacent sequences:  A169715 A169716 A169717 * A169719 A169720 A169721

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 20 2010

STATUS

approved

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Last modified December 6 04:43 EST 2019. Contains 329784 sequences. (Running on oeis4.)