A001306 Number of ways of making change for n cents using coins of 1, 5, 10, 20, 50, 100 cents.

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 14, 14, 14, 14, 14, 20, 20, 20, 20, 20, 26, 26, 26, 26, 26, 35, 35, 35, 35, 35, 44, 44, 44, 44, 44, 57, 57, 57, 57, 57, 70, 70, 70, 70, 70, 88, 88, 88, 88, 88, 106, 106, 106, 106

Offset

0,6

Comments

Number of partitions of n into parts 1, 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 179

Index entries for linear recurrences with constant coefficients, order 186.

Index entries for sequences related to making change.

Formula

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

Mathematica

CoefficientList[ Series[ 1 / ((1 - x)(1 - x^5)(1 - x^10)(1 - x^20)(1 - x^50)(1 - x^100)), {x, 0, 60} ], x ]

Crossrefs

Sequence in context: A001299 A001300 A169718 * A260984 A108105 A321213

Adjacent sequences: A001303 A001304 A001305 * A001307 A001308 A001309

Keyword

nonn

Author

N. J. A. Sloane

Status

approved