A001302 Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25, 50 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, 65, 71, 78, 84, 91, 102, 109, 120, 127, 138, 151, 162, 175, 186, 199, 217, 230, 248, 261, 279, 300, 318, 339, 357, 378, 407, 428, 457, 478, 507, 540, 569, 602, 631, 664

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5, 10, 25, 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 178

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, 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, 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, 0, 0, 0, 0, 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^25)*(1-x^50)).

a(n) = Sum_{k=0..floor(n/2)} A001300(n-2*k). - Christian Krause, Apr 24 2021

Mathematica

CoefficientList[ Series[ 1 / ((1 - x)(1 - x^2)(1 - x^5)(1 - x^10)(1 - x^25)(1 - x^50)), {x, 0, 55} ], x ]
Array[Length@IntegerPartitions[#, All, {1, 2, 5, 10, 25, 50}]&, 100, 0] (* Giorgos Kalogeropoulos, Apr 24 2021 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50))+ O(x^100)) \\ Michel Marcus, Sep 05 2014

Crossrefs

Sequence in context: A001312 A182086 A001301 * A001313 A057537 A339094

Adjacent sequences: A001299 A001300 A001301 * A001303 A001304 A001305

Keyword

nonn

Author

N. J. A. Sloane

Status

approved