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A145188
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Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) and a(1)=14
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10
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14, 2786, 21624372014, 10111847525912679844192131854786, 1033930953043290626825587838528711318150300040875029341893199068078185510802565166824630504014
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| General formula for continued cotangent recurrences type:
a(n+1)=a(n)3+3*a(n) and a(1)=k is following:
a(n)=Floor[((k+Sqrt[k^2+4])/2)^(3^(n-1))]
k=1 see A006267
k=2 see A006266
k=3 see A006268
k=4 see A006267(n+1)
k=5 see A006269
k=6 see A145180
k=7 see A145181
k=8 see A145182
k=9 see A145183
k=10 see A145184
k=11 see A145185
k=12 see A145186
k=13 see A145187
k=14 see A145188
k=15 see A145189
Essentially the same as A006266. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009]
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FORMULA
| a(n+1)=a(n)3+3*a(n) and a(1)=14
a(n)=Floor[((14+Sqrt[14^2+4])/2)^(3^(n-1))]
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MATHEMATICA
| a = {}; k = 14; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a
or
Table[Floor[((14 + Sqrt[200])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)
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CROSSREFS
| A006267, A006266, A006268, A006269, A145180, A145181, A145182, A145183, A145184, A145185, A145186, A145187, A145188, A145189
Sequence in context: A079918 A199648 A013719 * A064075 A206627 A188955
Adjacent sequences: A145185 A145186 A145187 * A145189 A145190 A145191
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Oct 03 2008
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