A145276 a(n) = A145233(n+1)/A145233(n).

1866294, 41473935220454958813340461622291147206

Offset: 1

Author

Artur Jasinski, Oct 06 2008

Keywords

• nonn
• bref

Comments

A member of the family of sequences of type:

(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + sqrt(5))/2.

For k=2 see A001566.

For k=3 see A002814(n+2).

For k=4 see A145274.

For k=5 see A145275.

For k=6 see this sequence.

For k=7 see A145277.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3

Crossrefs

Cf. A001566, A001622, A002814, A145233, A145274, A145275, A145277.

Programs

Mathematica

G = (1 + Sqrt[5])/2; Table[Expand[(G^(6^(n + 1)) - (1 - G)^(6^(n + 1)))/Sqrt[5]]/Expand[(G^(6^n) - (1 - G)^(6^n))/Sqrt[5]], {n, 1, 5}]

Formula

a(n) = (G^(6^(n + 1)) - (1 - G)^(6^(n + 1)))/(G^(6^n) - (1 - G)^(6^n)) where G = (1 + sqrt(5))/2.