A001314 Number of (unordered) ways of making change for n cents using coins of 2, 5 (two kinds), 10, 20, 50 cents.
1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 5, 2, 5, 2, 5, 8, 5, 8, 5, 8, 15, 8, 15, 8, 15, 22, 15, 22, 15, 22, 35, 22, 35, 22, 35, 48, 35, 48, 35, 48, 70, 48, 70, 48, 70, 92, 70, 92, 70, 92, 127, 92, 127, 92, 127, 162, 127, 162, 127, 162, 215, 162, 215, 162, 215, 268
Offset: 0
Keywords
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.
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 183
- Index entries for sequences related to making change.
- Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, 0, -1).
Programs
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Maple
1/(1-x^2)/(1-x^5)^2/(1-x^10)/(1-x^20)/(1-x^50)
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Mathematica
CoefficientList[Series[1/((1 - x^2) (1 - x^5)^2 (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x] Table[Length[FrobeniusSolve[{2,5,5,10,20,50},n]],{n,0,70}] (* Harvey P. Dale, Sep 23 2023 *)