OFFSET
0,6
COMMENTS
Number of partitions of n into parts 1, 5, 10, 25, 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..10000
M. Erickson, Change for a dollar, change for a million, Math. Horizons, Feb 2010, pp. 22-25.
B. Polster, Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions), Mathologer video (2021).
FORMULA
G.f.: 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)*(1-x^100)).
MATHEMATICA
Table[Length[FrobeniusSolve[{1, 5, 10, 25, 50, 100}, n]], {n, 0, 80}] (* or *) CoefficientList[Series[1/((1-x)(1-x^5)(1-x^10)(1-x^25)(1-x^50)(1-x^100)), {x, 0, 80}], x] (* Harvey P. Dale, Dec 25 2011 *)
PROG
(Haskell)
a169718 = p [1, 5, 10, 25, 50, 100] where
p _ 0 = 1
p [] _ = 0
p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Dec 15 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 20 2010
STATUS
approved