A250495 -id:A250495 - cp's OEIS frontend

A008973 Fibonacci number F(n) to power F(n).

1, 1, 1, 4, 27, 3125, 16777216, 302875106592253, 5842587018385982521381124421, 11756638905368616011414050501310355554617941909569536, 524744532468751923546122657597368049278513737089035272057324643668607677682302892208099365234375

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..14

Cf. A000045, A000312, A250495.

with(combinat):
[ seq(fibonacci(n)^fibonacci(n), n=0..15) ];

Table[f=Fibonacci[n];f^f,{n,0,9}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *)

a(n)=my(f=fibonacci(n)); f^f \\ Charles R Greathouse IV, Oct 03 2016

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

a(n) = A000312(A000045(n)).

A250486 A(n,k) is the n^k-th Fibonacci number; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 2, 1, 0, 1, 21, 34, 3, 1, 0, 1, 987, 196418, 987, 5, 1, 0, 1, 2178309, 37889062373143906, 10610209857723, 75025, 8, 1

Offset: 0

Alois P. Heinz, Nov 24 2014

			Square array A(n,k) begins:
  1,  0,  0,      0,       0,    0,  0,  0,   ...
  1,  1,  1,      1,       1,    1,  1,  1,   ...
  1,  1,  3,      21,      987,  2178309,     ...
  1,  2,  34,     196418,  37889062373143906, ...
  1,  3,  987,    10610209857723,             ...
  1,  5,  75025,  59425114757512643212875125, ...
  1,  8,  14930352,                           ...
  1,  13, 7778742049,                         ...

Alois P. Heinz, Antidiagonals n = 0..10, flattened
Wikipedia, Fibonacci number

Columns k=0-8 give: A000012, A000045, A054783, A182149, A250490, A250491, A250492, A250493, A250494.
Rows n=0-10 give: A000007, A000012, A058635, A045529, A145231, A145232, A145233, A145234, A250487, A250488, A250489.
Main diagonal gives A250495.
Cf. A000045.

A:= (n, k)-> (<<0|1>, <1|1>>^(n^k))[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..8);

A[n_, k_] := MatrixPower[{{0, 1}, {1, 1}}, n^k][[1, 2]]; A[0, 0] = 1;
Table[A[n, d-n], {d, 0, 8}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 28 2019, from Maple *)

A(n,k) = [0, 1; 1, 1]^(n^k)[1,2].

cp's OEIS Frontend

A008973 Fibonacci number F(n) to power F(n).

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