A358206 Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents.

1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 13, 13, 18, 18, 24, 24, 31, 31, 39, 39, 50, 50, 62, 62, 77, 77, 93, 93, 112, 112, 134, 134, 159, 159, 187, 187, 218, 218, 252, 252, 292, 292, 335, 335, 384, 384, 436, 436, 494, 494, 558, 558, 628, 628, 704, 704, 786, 786, 874, 874, 972, 972

Offset

0,3

Comments

Number of ways of making change for 50n Colombian pesos using coins of 50, 100, 200, 500 and 1000 pesos.

Number of partitions of n into parts 1,2,4,10 and 20.

Links

Table of n, a(n) for n=0..61.

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, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 1, -1, -1, 1).

Formula

G.f.: 1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20)).

a(n) = A000064(floor(n/2)).

a(n) ~ n^4/38400.

Example

a(5)=4 counts the ways of making change for 5 cents, these are (1,1,1,1,1), (1,1,1,2), (1,2,2), (1,4).

Mathematica

A[x_]:=1/((1 - x) (1 - x^2) (1 - x^4) (1 - x^10) (1 - x^20));
a[n_]:=SeriesCoefficient[A[x], {x, 0, n}]

Crossrefs

Cf. A000064, A001310.

Sequence in context: A029010 A060027 A001362 * A001310 A328422 A029009

Adjacent sequences: A358203 A358204 A358205 * A358207 A358208 A358209

Keyword

nonn,easy

Author

Daniel Checa, Nov 03 2022

Status

approved