A001313 Number of ways of making change for n cents using coins of 1, 2, 5, 10, 20, 50 cents.

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 41, 44, 51, 54, 61, 68, 75, 82, 89, 96, 109, 116, 129, 136, 149, 162, 175, 188, 201, 214, 236, 249, 271, 284, 306, 328, 350, 372, 394, 416, 451, 473, 508, 530, 565, 600, 635, 670, 705, 740

Offset

0,3

Comments

Number of partitions of n into parts 1, 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

H. Bottomley, Initial terms of A000008, A001301, A001302, A001312, A001313

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 182

Index entries for sequences related to making change.

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1).

Formula

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)).

Mathematica

CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x]
Table[Length[FrobeniusSolve[{1, 2, 5, 10, 20, 50}, n]], {n, 0, 60}] (* (very slow) Harvey P. Dale, Dec 25 2011 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^50))+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

Crossrefs

Cf. A001319.

Sequence in context: A182086 A001301 A001302 * A057537 A339094 A286874

Adjacent sequences: A001310 A001311 A001312 * A001314 A001315 A001316

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved