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A001301
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Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25 cents.
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6
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1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 40, 43, 49, 52, 58, 65, 71, 78, 84, 91, 102, 109, 120, 127, 138, 151, 162, 175, 186, 199, 217, 230, 248, 261, 279, 300, 318, 339, 357, 378, 406, 427, 455, 476, 504, 536, 564, 596, 624, 656
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OFFSET
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0,3
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COMMENTS
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Number of partitions of n into parts 1, 2, 5, 10, and 25. - Joerg Arndt, Sep 05 2014
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REFERENCES
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1).
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FORMULA
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G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^25)).
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MAPLE
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M := Matrix(43, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 2, 5, 8, 10, 13, 16, 17, 25, 28, 31, 32, 36, 37, 40, 43])) then 1 elif j=1 and member(i, [3, 6, 7, 11, 12, 15, 18, 26, 27, 30, 33, 35, 38, 41, 42]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..51); # Alois P. Heinz, Jul 25 2008
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MATHEMATICA
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CoefficientList[ Series[ 1 / ((1 - x)(1 - x^2)(1 - x^5)(1 - x^10)(1 - x^25)), {x, 0, 55} ], x ]
Table[Length[FrobeniusSolve[{1, 2, 5, 10, 25}, n]], {n, 0, 60}] (* Harvey P. Dale, Jan 19 2020 *)
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PROG
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(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^25)) + O(x^100)) \\ Michel Marcus, Sep 05 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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