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A001364 Number of ways of making change for n cents using coins of 1, 2, 4, 12, 24, 48, 96, 120 cents (based on English coinage of 1939). 2
1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 12, 12, 17, 17, 22, 22, 29, 29, 36, 36, 45, 45, 54, 54, 67, 67, 80, 80, 97, 97, 114, 114, 135, 135, 156, 156, 183, 183, 210, 210, 243, 243, 276, 276, 315, 315, 354, 354, 403, 403, 452, 452, 511, 511, 570, 570, 639, 639, 708, 708 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

More precisely number of ways of making change for n farthings. The coins were farthing, halfpenny, penny, threepence, sixpence, shilling, florin, half-crown.

Number of partitions of n into parts 1, 2, 4, 12, 24, 48, 96, and 120. - Joerg Arndt, Sep 05 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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, order 307.

Index entries for sequences related to making change.

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^12)*(1-x^24)*(1-x^48)*(1-x^96)*(1-x^120)).

MATHEMATICA

nn = 60; CoefficientList[Series[1/((1 - x^1) (1 - x^2) (1 - x^4) (1 - x^12) (1 - x^24) (1 - x^48) (1 - x^96) (1 - x^120)), {x, 0, nn}], x]

CROSSREFS

Sequence in context: A238132 A278296 A008642 * A029010 A060027 A001362

Adjacent sequences:  A001361 A001362 A001363 * A001365 A001366 A001367

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 22 05:52 EST 2018. Contains 317453 sequences. (Running on oeis4.)