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

0,6

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

Formula

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

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 *)

Crossrefs

Cf. A114138, A073031, A114140.

Sequence in context: A200445 A255362 A017833 * A351724 A113444 A228669

Adjacent sequences: A114041 A114042 A114043 * A114045 A114046 A114047

Keyword

nonn,easy

Author

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

Status

approved