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The number of ways of making change for 5n cents with Canadian coins (5, 10, 25, 100, 200).
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%I #32 Nov 22 2023 11:16:41

%S 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,

%T 50,54,58,62,68,72,78,82,88,94,100,106,112,118,128,134,144,150,160,

%U 170,180,190,200,210,224,234,248,258,272,286,300,314,328,342,362

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

%C 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).

%C Number of partitions of n into parts 1, 2, 5, 20, 40. - _Alois P. Heinz_, Nov 11 2023

%H Ray Chandler, <a href="/A367253/b367253.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_68">Index entries for linear recurrences with constant coefficients</a>, 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).

%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>

%F From _Alois P. Heinz_, Nov 11 2023: (Start)

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

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

%t a[n_]:=Length[FrobeniusSolve[{5,10,25,100,200},5*n]]; a/@Range[0,100] (* _Ivan N. Ianakiev_, Nov 21 2023 *)

%t 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 *)

%Y Cf. A000008, A001312, A182086, A307849.

%K nonn,easy

%O 0,3

%A _Johann Peters_, Nov 11 2023