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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). 3

%I

%S 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,

%T 80,80,97,97,114,114,135,135,156,156,183,183,210,210,243,243,276,276,

%U 315,315,354,354,403,403,452,452,511,511,570,570,639,639,708,708

%N 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).

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

%C Number of partitions of n into parts 1, 2, 4, 12, 24, 48, 96, and 120. - _Joerg Arndt_, Sep 05 2014

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.

%D G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.

%H T. D. Noe, <a href="/A001364/b001364.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_307">Index entries for linear recurrences with constant coefficients</a>, order 307.

%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>

%F 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)).

%t 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]

%K nonn

%O 0,3

%A _N. J. A. Sloane_

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Last modified October 4 04:26 EDT 2022. Contains 357237 sequences. (Running on oeis4.)