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%I #12 Feb 09 2024 17:21:24
%S 10,20,30,40,5,60,70,80,90,10,110,120,130,140,15,160,170,180,190,20,
%T 210,220,230,240,25,260,270,280,290,30,310,320,330,340,35,360,370,380,
%U 390,40,410,420,430,440,45,460,470,480,490,50,510,520,530,540,55,560
%N Smallest multiple of 5 beginning with n.
%H Vincenzo Librandi, <a href="/A237416/b237416.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F G.f.: 5*x*(2 +4*x +6*x^2 +8*x^3 +x^4 +8*x^5 +6*x^6 +4*x^7 +2*x^8)/(1 -x^5)^2.
%F a(n) = 2*a(n-5) - a(n-10).
%t Table[If[Mod[n, 5]==0, n, If[Mod[10 n, 5]==0, 10 n, 10 n + 5 - Mod[10 n, 5]]], {n, 60}] (* or *) CoefficientList[Series[5 (2 + 4 x + 6 x^2 + 8 x^3 + x^4 + 8 x^5 + 6 x^6 + 4 x^7 + 2 x^8)/(1 - x^5)^2, {x, 0, 40}], x]
%o I:=[10,20,30,40,5,60,70,80,90,10]; [n le 10 select I[n] else 2*Self(n-5)-Self(n-10): n in [1..60]];
%Y Cf. A082799, A082800, A082801, A082802, A082803, A082804.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 10 2014
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