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).

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

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: A332305 A340282 A008642 * A029010 A060027 A001362

Adjacent sequences: A001361 A001362 A001363 * A001365 A001366 A001367

Keyword

nonn

Author

N. J. A. Sloane

Status

approved