A177849 The number of ways of minimal weight to make change for n cents using fairly valued United States coins (copper 1-cent coin, a nickel 5-cent coin, and silver 10-cent and 25-cent coins) assuming that silver is more valuable than nickel and that nickel is more valuable than copper.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3

Offset

0,51

Links

Table of n, a(n) for n=0..104.

Formula

G.f.: [1/(1-x^10)/(1-x^25)+x^5+x^15][1+x+x^2+x^3+x^4]

Example

For n = 51 cents, the least weight is achieved with 50 cents in silver and 1 cent in copper. The 50 cents in silver can be achieved as two 25-cent coins or five 10-cent coins; thus there are a(51) = 2 ways to make 51 cents with minimal weight.

Crossrefs

Except for the values dependent upon nickel (i.e., a(5) through a(9) and a(15) through a(19)) this sequence can be constructed by repeating five times each term from sequence A008616.

Sequence in context: A063059 A214564 A102675 * A143544 A031346 A335808

Adjacent sequences: A177846 A177847 A177848 * A177850 A177851 A177852

Keyword

easy,nonn

Author

Lee A. Newberg, May 14 2010

Status

approved