A367253 The number of ways of making change for 5n cents with Canadian coins (5, 10, 25, 100, 200).

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 20, 22, 24, 26, 30, 32, 36, 38, 42, 46, 50, 54, 58, 62, 68, 72, 78, 82, 88, 94, 100, 106, 112, 118, 128, 134, 144, 150, 160, 170, 180, 190, 200, 210, 224, 234, 248, 258, 272, 286, 300, 314, 328, 342, 362

Offset: 0

Author

Johann Peters, Nov 11 2023

Keywords

• nonn
• easy

Comments

Since 2012 the Canadian penny has been discontinued. The coins now commonly used are the nickel (5 cents), the dime (10 cents), the quarter (25 cents), the loonie (100 cents), and the toonie (200 cents).

Number of partitions of n into parts 1, 2, 5, 20, 40. - Alois P. Heinz, Nov 11 2023

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1).
• Index entries for sequences related to making change.

Crossrefs

Cf. A000008, A001312, A182086, A307849.

Programs

Mathematica

a[n_]:=Length[FrobeniusSolve[{5,10,25,100,200},5*n]]; a/@Range[0,100] (* Ivan N. Ianakiev, Nov 21 2023 *)
CoefficientList[Series[1/((1-x)*(1-x^2)*(1-x^5)*(1-x^20)*(1-x^40)),{x,0,1000}],x] (* Ray Chandler, Nov 22 2023 *)

Formula

From Alois P. Heinz, Nov 11 2023: (Start)

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^20)*(1-x^40)).

a(20*n) = A307849(n). (End)