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 A001300 Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents. 10
 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, 18, 18, 18, 18, 24, 24, 24, 24, 24, 31, 31, 31, 31, 31, 39, 39, 39, 39, 39, 50, 50, 50, 50, 50, 62, 62, 62, 62, 62, 77, 77, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Number of partitions of n into parts 1, 5, 10, 25, and 50. - Joerg Arndt, May 10 2014 a(n) = A001299(n) for n < 50; a(n) = A169718(n) for n < 100. - Reinhard Zumkeller, Dec 15 2013 REFERENCES R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316. G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1, Problems 1 and 2. LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 176 Index entries for linear recurrences with constant coefficients, 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). FORMULA G.f.: 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)). MAPLE 1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)*(1-x^50)); MATHEMATICA CoefficientList[ Series[ 1 / ((1 - x)(1 - x^5)(1 - x^10)(1 - x^25)(1 - x^50)), {x, 0, 65} ], x ] PROG (Haskell) a001300 = p [1, 5, 10, 25, 50] where    p _          0 = 1    p []         _ = 0    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m -- Reinhard Zumkeller, Dec 15 2013 (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 CROSSREFS Cf. A001299, A169718, A000008. Sequence in context: A130496 A187243 A001299 * A169718 A001306 A260984 Adjacent sequences:  A001297 A001298 A001299 * A001301 A001302 A001303 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Mar 15 1996 STATUS approved

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Last modified June 21 11:18 EDT 2021. Contains 345362 sequences. (Running on oeis4.)