A145187 - OEIS

%I #7 Mar 31 2012 10:22:10

%S 13,2236,11179326964,1397162674037779847605429310236,

%T 2727350312258670490076364505418491429134385511825631286349491134548728023756939667650354964

%N Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) with a(1)=13.

%C General formula for continued cotangent recurrences of the form a(n+1)=a(n)^3+3*a(n) with a(1)=k is a(n)=floor(((k+sqrt(k^2+4))/2)^(3^(n-1))).

%C For k=1 see A006267

%C k=2 see A006266

%C k=3 see A006268

%C k=4 see A006267(n+1)

%C k=5 see A006269

%C k=6 see A145180

%C k=7 see A145181

%C k=8 see A145182

%C k=9 see A145183

%C k=10 see A145184

%C k=11 see A145185

%C k=12 see A145186

%C k=13 see A145187

%C k=14 see A145188

%C k=15 see A145189

%F a(n+1)=a(n)^3+3*a(n) and a(1)=13

%F a(n)=Floor[((13+Sqrt[13^2+4])/2)^(3^(n-1))]

%t a = {}; k = 13; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a

%t or

%t Table[Floor[((13 + Sqrt[173])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)

%Y Cf. A006267, A006266, A006268, A006269, A145180, A145181, A145182, A145183, A145184, A145185, A145186, A145187, A145188, A145189

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 03 2008