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

0,3

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.

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)

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 *)

Crossrefs

Cf. A000008, A001312, A182086, A307849.

Sequence in context: A274165 A011874 A000115 * A033552 A062420 A089197

Adjacent sequences: A367250 A367251 A367252 * A367254 A367255 A367256

Keyword

nonn,easy

Author

Johann Peters, Nov 11 2023

Status

approved