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A001300 Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents. 8

%I

%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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Last modified November 14 07:29 EST 2019. Contains 329111 sequences. (Running on oeis4.)