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

%I A367253 #32 Nov 22 2023 11:16:41
%S A367253 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 A367253 50,54,58,62,68,72,78,82,88,94,100,106,112,118,128,134,144,150,160,
%U A367253 170,180,190,200,210,224,234,248,258,272,286,300,314,328,342,362
%N A367253 The number of ways of making change for 5n cents with Canadian coins (5, 10, 25, 100, 200).
%C A367253 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 A367253 Number of partitions of n into parts 1, 2, 5, 20, 40. - _Alois P. Heinz_, Nov 11 2023
%H A367253 Ray Chandler, <a href="/A367253/b367253.txt">Table of n, a(n) for n = 0..1000</a>
%H A367253 <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 A367253 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%F A367253 From _Alois P. Heinz_, Nov 11 2023: (Start)
%F A367253 G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^20)*(1-x^40)).
%F A367253 a(20*n) = A307849(n). (End)
%t A367253 a[n_]:=Length[FrobeniusSolve[{5,10,25,100,200},5*n]]; a/@Range[0,100] (* _Ivan N. Ianakiev_, Nov 21 2023 *)
%t A367253 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 A367253 Cf. A000008, A001312, A182086, A307849.
%K A367253 nonn,easy
%O A367253 0,3
%A A367253 _Johann Peters_, Nov 11 2023