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A001362 Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents. 1
1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 13, 13, 18, 18, 24, 24, 31, 31, 39, 39, 49, 49, 60, 60, 73, 73, 87, 87, 103, 103, 121, 121, 141, 141, 163, 163, 187, 187, 213, 213, 242, 242, 273, 273, 307, 307, 343, 343, 382, 382, 424, 424, 469, 469, 517, 517, 568, 568, 622, 622 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1, 2, 4, and 10. - 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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 186

Index entries for sequences related to making change.

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 1, -1, -1, 1, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1).

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^10)).

MAPLE

1/(1-x)/(1-x^2)/(1-x^4)/(1-x^10): seq(coeff(series(%, x, n+1), x, n), n=0..80);

MATHEMATICA

nn = 1000; CoefficientList[Series[1/((1 - x^1) (1 - x^2) (1 - x^4) (1 - x^10)), {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)

PROG

(PARI) a(n)=floor((n\2+8)*(2*(n\2)^2+11*(n\2)+18)/120) \\ Tani Akinari, May 14 2014

CROSSREFS

Twice A001304.

Sequence in context: A001364 A029010 A060027 * A001310 A029009 A023023

Adjacent sequences:  A001359 A001360 A001361 * A001363 A001364 A001365

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 14 17:12 EST 2018. Contains 317210 sequences. (Running on oeis4.)