A250488 a(n) = Fibonacci(9^n).

1, 34, 37889062373143906

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3

Formula

a(n) = A000045(9^n).

From Peter Bala, Nov 25 2022: (Start)

a(n+1) = 625*a(n)^9 - 1125*a(n)^7 + 675*a(n)^5 - 150*a(n)^3 + 9*a(n) with a(0) = 1.

a(n) == 7 (mod 9) for n >= 1.

a(n+1) == a(n) mod (9^n).

5*a(n)^2 == 2 (mod 9^n).

In the ring of 9-adic integers, the sequence {a(n)} is a Cauchy sequence. It converges to a 9-adic root of the quadratic equation 5*x^2 - 2 = 0 (the 9-adic Cauchy sequence {Fibonacci(3*9^n)} converges to the other root). (End)

Maple

a:= n-> (<<0|1>, <1|1>>^(9^n))[1, 2]:
seq(a(n), n=0..4);

Crossrefs

Row n = 9 of A250486. Bisection of A045529.

Cf. A000045.

Sequence in context: A279376 A189311 A189253 * A236237 A067156 A365894

Adjacent sequences: A250485 A250486 A250487 * A250489 A250490 A250491

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 24 2014

Status

approved