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A001319 Number of (unordered) ways of making change for n cents using coins of 2, 5, 10, 20, 50 cents.

%I A001319 #32 Feb 01 2022 01:30:31
%S A001319 1,0,1,0,1,1,1,1,1,1,3,1,3,1,3,3,3,3,3,3,7,3,7,3,7,7,7,7,7,7,13,7,13,
%T A001319 7,13,13,13,13,13,13,22,13,22,13,22,22,22,22,22,22,35,22,35,22,35,35,
%U A001319 35,35,35,35,53,35,53,35,53,53,53,53,53,53,77,53,77
%N A001319 Number of (unordered) ways of making change for n cents using coins of 2, 5, 10, 20, 50 cents.
%C A001319 Number of partitions of n into parts 2, 5, 10, 20, and 50. - _Joerg Arndt_, Sep 05 2014
%D A001319 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.
%D A001319 G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.
%H A001319 T. D. Noe, <a href="/A001319/b001319.txt">Table of n, a(n) for n = 0..1000</a>
%H A001319 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=184">Encyclopedia of Combinatorial Structures 184</a>
%H A001319 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A001319 <a href="/index/Rec#order_87">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1).
%p A001319 1/(1-x^2)/(1-x^5)/(1-x^10)/(1-x^20)/(1-x^50)
%t A001319 CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x]
%Y A001319 First differences of A001313.
%K A001319 nonn
%O A001319 0,11
%A A001319 _N. J. A. Sloane_