login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001310 Number of ways of making change for n cents using coins of 1, 2, 4, 10, 20, 40, 100 cents. 1
1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 13, 13, 18, 18, 24, 24, 31, 31, 39, 39, 50, 50, 62, 62, 77, 77, 93, 93, 112, 112, 134, 134, 159, 159, 187, 187, 218, 218, 252, 252, 293, 293, 337, 337, 388, 388, 442, 442, 503, 503, 571, 571, 646, 646, 728, 728, 817, 817, 913 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1, 2, 4, 10, 20, 40, 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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 180

Index entries for linear recurrences with constant coefficients, order 177.

Index entries for sequences related to making change.

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^10)*(1-x^20)*(1-x^40)*(1-x^100)).

EXAMPLE

1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 6*x^6 + 6*x^7 + 9*x^8 + 9*x^9 + 13*x^10 + ...

MATHEMATICA

a[n_] := SeriesCoefficient[1/((1 - x)(1 - x^2)(1 - x^4)(1 - x^10)(1 - x^40)(1 - x^100)), {x, 0, n}]

Table[Length[FrobeniusSolve[{1, 2, 4, 10, 20, 40, 100}, n]], {n, 0, 60}] (* Harvey P. Dale, Nov 13 2013 *)

CROSSREFS

Sequence in context: A029010 A060027 A001362 * A029009 A023023 A184157

Adjacent sequences:  A001307 A001308 A001309 * A001311 A001312 A001313

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 21 09:13 EST 2018. Contains 317431 sequences. (Running on oeis4.)