cp's OEIS Frontend

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

%I A057537 #33 Nov 30 2023 00:54:20
%S A057537 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,
%T A057537 75,82,89,96,109,116,129,136,149,162,175,188,201,214,236,249,271,284,
%U A057537 306,328,350,372,394,416,451,473,508,530,565,600,635,670,705,740,793,828
%N A057537 Number of ways of making change for n Euro-cents using the Euro currency.
%C A057537 Euro currency has coins and bills of size 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000 cents.
%C A057537 Differs from A001313 first at n=100. - _Georg Fischer_, Oct 06 2018
%D A057537 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.
%D A057537 G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.
%H A057537 Alois P. Heinz, <a href="/A057537/b057537.txt">Table of n, a(n) for n = 0..65536</a>
%H A057537 AFP, <a href="https://www.france24.com/en/20181231-500-euro-note-gets-last-print-run">500-euro note gets last print run</a>, (2019)
%H A057537 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A057537 <a href="/index/Rec#order_88888">Index entries for linear recurrences with constant coefficients</a>, order 88888.
%F A057537 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)).
%p A057537 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)):
%p A057537 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A057537 seq(a(n), n=0..100);
%t A057537 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 *)
%o A057537 (PARI) coins(v[..])=my(x='x); prod(i=1,#v,1/(1-x^v[i]))
%o A057537 Vec(coins(1, 2, 5, 10, 20, 50, 100, 200)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 24 2022
%Y A057537 Cf. A001313.
%K A057537 nonn,easy
%O A057537 0,3
%A A057537 Thomas Brendan Murphy (murphybt(AT)tcd.ie), Sep 06 2000