cp's OEIS Frontend

A145181 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) and a(1)=7.

%I A145181 #9 Jun 02 2025 00:37:29
%S A145181 7,364,48229636,112186849649044142700364,
%T A145181 1411971263214164889494039458947084336929208169473485667118006013929636
%N A145181 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) and a(1)=7.
%C A145181 General formula for continued cotangent recurrences type:
%C A145181 a(n+1)=a(n)3+3*a(n) and a(1)=k is following:
%C A145181 a(n)=Floor[((k+Sqrt[k^2+4])/2)^(3^(n-1))]
%C A145181 k=1 see A006267
%C A145181 k=2 see A006266
%C A145181 k=3 see A006268
%C A145181 k=4 see A006267(n+1)
%C A145181 k=5 see A006269
%C A145181 k=6 see A145180
%C A145181 k=7 see A145181
%C A145181 k=8 see A145182
%C A145181 k=9 see A145183
%C A145181 k=10 see A145184
%C A145181 k=11 see A145185
%C A145181 k=12 see A145186
%C A145181 k=13 see A145187
%C A145181 k=14 see A145188
%C A145181 k=15 see A145189
%F A145181 a(n+1)=a(n)^3 + 3*a(n) and a(1)=7
%F A145181 a(n)=Floor[((7+Sqrt[7^2+4])/2)^(3^(n-1))]
%t A145181 a = {}; k = 7; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a
%t A145181 or
%t A145181 Table[Floor[((7 + Sqrt[53])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)
%Y A145181 A006267, A006266, A006268, A006269, A145180, A145181, A145182, A145183, A145184, A145185, A145186, A145187, A145188, A145189
%K A145181 nonn
%O A145181 1,1
%A A145181 _Artur Jasinski_, Oct 03 2008