A001312 Number of ways of making change for n cents using coins of 1, 2, 5, 10, 50, 100 cents.

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 40, 43, 49, 52, 58, 64, 70, 76, 82, 88, 98, 104, 114, 120, 130, 140, 150, 160, 170, 180, 195, 205, 220, 230, 245, 260, 275, 290, 305, 320, 342, 357, 379, 394, 416, 438, 460, 482, 504, 526

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5, 10, 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

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 181

Index entries for linear recurrences with constant coefficients, order 168.

Index entries for sequences related to making change.

Formula

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^50)*(1-x^100)).

Example

1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 7*x^8 + 8*x^9 + 11*x^10 + ...

Mathematica

a[ n_] := SeriesCoefficient[1/((1 - x)(1 - x^2)(1 - x^5)(1 - x^10)(1 - x^50)(1 - x^100)), {x, 0, n}]
Table[Length[FrobeniusSolve[{1, 2, 5, 10, 50, 100}, n]], {n, 0, 60}] (* Harvey P. Dale, Dec 29 2017 *)

Crossrefs

Sequence in context: A121385 A029015 A000008 * A182086 A001301 A001302

Adjacent sequences: A001309 A001310 A001311 * A001313 A001314 A001315

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved