A057537 Number of ways of making change for n Euro-cents using the Euro currency.

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

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.

Index entries for linear recurrences with constant coefficients, order 88888.

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 *)

Prog

(PARI) coins(v[..])=my(x='x); prod(i=1, #v, 1/(1-x^v[i]))
Vec(coins(1, 2, 5, 10, 20, 50, 100, 200)+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

Crossrefs

Cf. A001313.

Sequence in context: A001301 A001302 A001313 * A339094 A286874 A065459

Adjacent sequences: A057534 A057535 A057536 * A057538 A057539 A057540

Keyword

nonn,easy

Author

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

Status

approved