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Number of ways of making change for n cents using coins of 1, 5, 10, 20, 50, 100 cents.
3

%I #30 Feb 03 2022 00:33:24

%S 1,1,1,1,1,2,2,2,2,2,4,4,4,4,4,6,6,6,6,6,10,10,10,10,10,14,14,14,14,

%T 14,20,20,20,20,20,26,26,26,26,26,35,35,35,35,35,44,44,44,44,44,57,57,

%U 57,57,57,70,70,70,70,70,88,88,88,88,88,106,106,106,106

%N Number of ways of making change for n cents using coins of 1, 5, 10, 20, 50, 100 cents.

%C Number of partitions of n into parts 1, 5, 10, 20, 50, and 100. - _Joerg Arndt_, Sep 05 2014

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.

%D G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.

%H T. D. Noe, <a href="/A001306/b001306.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=179">Encyclopedia of Combinatorial Structures 179</a>

%H <a href="/index/Rec#order_186">Index entries for linear recurrences with constant coefficients</a>, order 186.

%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>

%F G.f.: 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)*(1-x^100)).

%t CoefficientList[ Series[ 1 / ((1 - x)(1 - x^5)(1 - x^10)(1 - x^20)(1 - x^50)(1 - x^100)), {x, 0, 60} ], x ]

%K nonn

%O 0,6

%A _N. J. A. Sloane_