Search: id:A123004
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%I A123004
%S A123004 0,1,2,29,108,941,4582,32689,179928,1177081,6852362,43131749,257572548,
%T A123004 1593438821,9626191342,59088353209,358831489968,2194871810161,
%U A123004 13360530869522,81592856993069,497198985724188,3034219396275101
%N A123004 Scaled recursion, coefficient expansion and Binet for what I call a "Tin 
               mean": Characteristic polynomial :l = 2; m = 5; x^2-l*x/m-1.
%C A123004 To distinguish these from the "Lead" means as x^2-x/m-1 I call these 
               "tin" as being rationally closer to whole Integers and thus being 
               worth more? l=2; m=3; gives A002534
%D A123004 Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and 
               Number, World Scientific, 2002.
%F A123004 l = 2; m = 5; a(n) = l*a(n - 1)/m + a(n - 2) C.F.=x/(1 - 2 x/5 - x^2)
%F A123004 a(n)=((1+sqrt(26)^n-(1-sqrt(26))^n)/(2*sqrt(26)) [From Rolf Pleisch (r_pleisch(AT)gmx.ch), 
               Jul 06 2009]
%t A123004 (* coefficient expansion*) l = 2; m = 5; p[x_] := -1 - l*x/m + x^2 q[x_] 
               := ExpandAll[x^2*p[1/x]] Table[ SeriesCoefficient[ Series[x/q[x], 
               {x, 0, 30}], n]*m^(n - 1), {n, 0, 30}] (* Binet/ recursion *) f[n_Integer] 
               = Module[{a}, a[n] /. RSolve[{a[n] == l*a[n - 1]/m + a[n - 2], a[0] 
               == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] ; a = Table[Rationalize[N[f[n]*m^(n 
               - 1), 100], 0], {n, 0, 25}]
%Y A123004 Cf. A002534.
%Y A123004 Sequence in context: A031918 A101231 A141949 this_sequence A062618 A128842 
               A028883
%Y A123004 Adjacent sequences: A123001 A123002 A123003 this_sequence A123005 A123006 
               A123007
%K A123004 nonn,uned
%O A123004 1,3
%A A123004 Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006

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