OFFSET
0,6
COMMENTS
Number of partitions of n into parts 1, 5, 10, 25, and 50. - Joerg Arndt, May 10 2014
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 15 1996
STATUS
approved