A114140 Number of ordered sequences of coins (each of which has value 1, 2, 5, 10 or 20) which add to n.

1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5505, 9412, 16093, 27518, 47051, 80453, 137563, 235215, 402188, 687688, 1175860, 2010567, 3437810, 5878212, 10050981, 17185883, 29385638, 50245647, 85913568, 146901103, 251181919

Offset: 0

Author

David S. Johnson and N. J. A. Sloane, Feb 22 2006

Keywords

• nonn

Comments

Equivalently, number of sequences of coins (each of which has value 5, 10, 25, 50 or 100) which add to 5n.

Based on "silver" US coins as of Feb 22 2006.

Number of compositions of n into parts 1, 2, 5, 10, and 20. - Joerg Arndt, Sep 19 2014

Crossrefs

Cf. A073031, A114044, A114138.

Programs

Maple

A114140 := proc(n)
    coeftayl( 1/(1-(x+x^2+x^5+x^10+x^20)), x=0, n);
end proc:
seq(A114140(n), n=0..30); # Wesley Ivan Hurt, Sep 18 2014

Mathematica

CoefficientList[Series[1/(1 - (x + x^2 + x^5 + x^10 + x^20)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 18 2014 *)

Formula

G.f.: 1/(1-(x+x^2+x^5+x^10+x^20)).