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%I #40 Apr 18 2017 07:02:35
%S 1,1,1,1,1,2,2,2,2,2,4,4,4,4,4,6,6,6,6,6,9,9,9,9,9,13,13,13,13,13,18,
%T 18,18,18,18,24,24,24,24,24,31,31,31,31,31,39,39,39,39,39,50,50,50,50,
%U 50,62,62,62,62,62,77,77,77
%N Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents.
%C Number of partitions of n into parts 1, 5, 10, 25, and 50. - _Joerg Arndt_, May 10 2014
%C a(n) = A001299(n) for n < 50; a(n) = A169718(n) for n < 100. - _Reinhard Zumkeller_, Dec 15 2013
%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, Problems 1 and 2.
%H T. D. Noe, <a href="/A001300/b001300.txt">Table of n, a(n) for n = 0..10000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=176">Encyclopedia of Combinatorial Structures 176</a>
%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H <a href="/index/Rec#order_91">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1).
%F G.f.: 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)).
%p 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50));
%t CoefficientList[ Series[ 1 / ((1 - x)(1 - x^5)(1 - x^10)(1 - x^25)(1 - x^50)), {x, 0, 65} ], x ]
%o (Haskell)
%o a001300 = p [1,5,10,25,50] where
%o p _ 0 = 1
%o p [] _ = 0
%o p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o -- _Reinhard Zumkeller_, Dec 15 2013
%o (PARI) a(n)=floor(((n\5)^4+38*(n\5)^3+476*(n\5)^2+2185*(n\5)+3735)/2400+(n\5+1)*(-1)^(n\5)/160+(n\5\5+1)*[0,0,1,0,-1][n\5%5+1]/10) \\ _Tani Akinari_, May 10 2014
%Y Cf. A001299, A169718, A000008.
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_, Mar 15 1996
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