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

0,11

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).

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]

Crossrefs

First differences of A001313.

Sequence in context: A087822 A163378 A025810 * A240833 A110919 A281273

Adjacent sequences: A001316 A001317 A001318 * A001320 A001321 A001322

Keyword

nonn

Author

N. J. A. Sloane

Status

approved