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A057537 Number of ways of making change for n Euro-cents using the Euro currency. 1
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, 793, 828 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Euro currency has coins and bills of size 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000 cents.

Differs from A001313 first at n=100. - Georg Fischer, Oct 06 2018

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

Alois P. Heinz, Table of n, a(n) for n = 0..65536

AFP, 500-euro note gets last print run, (2019)

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^20) * (1-x^50) * (1-x^100) * (1-x^200) * (1-x^500) * (1-x^1000) * (1-x^2000) * (1-x^5000) * (1-x^10000) * (1-x^20000) * (1-x^50000)).

MAPLE

gf:= 1/expand((1-x) * (1-x^2) * (1-x^5) * (1-x^10) * (1-x^20) * (1-x^50) * (1-x^100) * (1-x^200) * (1-x^500) * (1-x^1000) * (1-x^2000) * (1-x^5000) * (1-x^10000) * (1-x^20000) * (1-x^50000)):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..100);

MATHEMATICA

f = 1/Times@@(1 - x^{1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000}); a[n_] := SeriesCoefficient[f, {x, 0, n}]; Table[a[n], {n, 1, 61}] (* Jean-François Alcover, Nov 28 2013, after Maple *)

CROSSREFS

Cf. A001313.

Sequence in context: A001301 A001302 A001313 * A286874 A065459 A011873

Adjacent sequences:  A057534 A057535 A057536 * A057538 A057539 A057540

KEYWORD

nonn

AUTHOR

Thomas Brendan Murphy (murphybt(AT)tcd.ie), Sep 06 2000

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)