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%I #35 Feb 01 2022 01:29:26
%S 1,1,2,2,3,4,5,6,7,8,11,12,15,16,19,22,25,28,31,34,40,43,49,52,58,64,
%T 70,76,82,88,98,104,114,120,130,140,150,160,170,180,195,205,220,230,
%U 245,260,275,290,305,320,342,357,379,394,416,438,460,482,504,526
%N Number of ways of making change for n cents using coins of 1, 2, 5, 10, 50, 100 cents.
%C Number of partitions of n into parts 1, 2, 5, 10, 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="/A001312/b001312.txt">Table of n, a(n) for n = 0..1000</a>
%H H. Bottomley, <a href="/A000008/a000008.gif">Initial terms of A000008, A001301, A001302, A001312, A001313</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=181">Encyclopedia of Combinatorial Structures 181</a>
%H <a href="/index/Rec#order_168">Index entries for linear recurrences with constant coefficients</a>, order 168.
%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%F G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^50)*(1-x^100)).
%e 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 7*x^8 + 8*x^9 + 11*x^10 + ...
%t a[ n_] := SeriesCoefficient[1/((1 - x)(1 - x^2)(1 - x^5)(1 - x^10)(1 - x^50)(1 - x^100)), {x, 0, n}]
%t Table[Length[FrobeniusSolve[{1,2,5,10,50,100},n]],{n,0,60}] (* _Harvey P. Dale_, Dec 29 2017 *)
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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