A001362 Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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).

Crossrefs

Twice A001304.

Programs

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 *)
Table[Length[FrobeniusSolve[{1,2,4,10},n]],{n,0,60}] (* Harvey P. Dale, May 20 2021 *)

PARI

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

Formula

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