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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Programs

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 ]

Formula

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