A114044 Number of (ordered) sequences of coins (each of which has value 1, 5, 10, 25, 50 or 100) which add to n.

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 13, 18, 24, 31, 42, 58, 80, 109, 146, 197, 268, 366, 499, 676, 916, 1243, 1690, 2299, 3122, 4237, 5751, 7811, 10614, 14418, 19580, 26587, 36106, 49043, 66614, 90473, 122869, 166866, 226632, 307810, 418060, 567784, 771122, 1047296, 1422396

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Based on US coins as of Feb 22 2006.

a(n) is the number of compositions (ordered partitions) of n into parts 1, 5, 10, 25, 50, and 100. - Joerg Arndt, Apr 19 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A114138, A073031, A114140.

Programs

Mathematica

CoefficientList[Series[1/(1 - (x + x^5 + x^10 + x^25 + x^50 + x^100)), {x, 0, 50}], x] (* Wesley Ivan Hurt, Apr 18 2017 *)

Formula

G.f.: 1/(1-(x + x^5 + x^10 + x^25 + x^50 + x^100)).