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).
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
KEYWORD
nonn,easy
AUTHOR
Johann Peters, Nov 11 2023
STATUS
approved