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a(n) = A145231(n+1)/A145231(n).
5

%I #11 Oct 19 2024 08:35:15

%S 329,10749959329,13354478338703157414450712411084788083329

%N a(n) = A145231(n+1)/A145231(n).

%C A member of the family of sequences of type:

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

%C For k=2 see A001566.

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

%C For k=4 see this sequence.

%C For k=5 see A145275.

%C For k=6 see A145276.

%C For k=7 see A145277.

%H Amiram Eldar, <a href="/A145274/b145274.txt">Table of n, a(n) for n = 1..5</a>

%F a(n) = (G^(4^(n + 1)) - (1 - G)^(4^(n + 1)))/(G^(4^n) - (1 - G)^(4^n)) where G = (1 + sqrt(5))/2.

%t G = (1 + Sqrt[5])/2; Table[Expand[(G^(4^(n + 1)) - (1 - G)^(4^(n + 1)))/Sqrt[5]]/Expand[(G^(4^n) - (1 - G)^(4^n))/Sqrt[5]], {n, 1, 5}]

%Y Cf. A001566, A002814, A145231, A145274, A145275, A145276, A145277.

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 06 2008