A001319 Number of (unordered) ways of making change for n cents using coins of 2, 5, 10, 20, 50 cents.

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 7, 3, 7, 3, 7, 7, 7, 7, 7, 7, 13, 7, 13, 7, 13, 13, 13, 13, 13, 13, 22, 13, 22, 13, 22, 22, 22, 22, 22, 22, 35, 22, 35, 22, 35, 35, 35, 35, 35, 35, 53, 35, 53, 35, 53, 53, 53, 53, 53, 53, 77, 53, 77

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of partitions of n into parts 2, 5, 10, 20, and 50. - 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 184
• Index entries for sequences related to making change.
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1).

Crossrefs

First differences of A001313.

Programs

Maple

1/(1-x^2)/(1-x^5)/(1-x^10)/(1-x^20)/(1-x^50)

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x]