cp's OEIS Frontend

A001314 Number of (unordered) ways of making change for n cents using coins of 2, 5 (two kinds), 10, 20, 50 cents.

%I A001314 #30 Sep 23 2023 16:46:00
%S A001314 1,0,1,0,1,2,1,2,1,2,5,2,5,2,5,8,5,8,5,8,15,8,15,8,15,22,15,22,15,22,
%T A001314 35,22,35,22,35,48,35,48,35,48,70,48,70,48,70,92,70,92,70,92,127,92,
%U A001314 127,92,127,162,127,162,127,162,215,162,215,162,215,268
%N A001314 Number of (unordered) ways of making change for n cents using coins of 2, 5 (two kinds), 10, 20, 50 cents.
%D A001314 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.
%D A001314 G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.
%H A001314 T. D. Noe, <a href="/A001314/b001314.txt">Table of n, a(n) for n = 0..1000</a>
%H A001314 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=183">Encyclopedia of Combinatorial Structures 183</a>
%H A001314 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A001314 <a href="/index/Rec#order_92">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, 0, -1).
%p A001314 1/(1-x^2)/(1-x^5)^2/(1-x^10)/(1-x^20)/(1-x^50)
%t A001314 CoefficientList[Series[1/((1 - x^2) (1 - x^5)^2 (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x]
%t A001314 Table[Length[FrobeniusSolve[{2,5,5,10,20,50},n]],{n,0,70}] (* _Harvey P. Dale_, Sep 23 2023 *)
%K A001314 nonn
%O A001314 0,6
%A A001314 _N. J. A. Sloane_