A370223 AGM transform of the positive Fibonacci numbers.

0, 0, 10, 865, 155082, 52802560, 40048988817, 71202718146816, 315615332953930528, 3574469013941010577249, 104798469697184132865547168, 7984603919946049180938300030976, 1584983603576817306123611193840098529, 820874582413458038007335015822715588591616

Offset

1,3

Comments

See A368366 for the description of the AGM transform.

Links

Paolo Xausa, Table of n, a(n) for n = 1..68

Formula

a(n) = A000071(n+2)^n - A000312(n)*A003266(n).

Mathematica

A370223[n_] := (Fibonacci[n+2]-1)^n - n^n*Fibonorial[n]; Array[A370223, 15]

Prog

(Python)
from itertools import count, islice
def A370223_gen(): # generator of terms
    a, b, s, p = 1, 1, 0, 1
    for n in count(1):
        s += a
        p *= a
        yield s**n-n**n*p
        a, b = b, a+b
A370223_list = list(islice(A370223_gen(), 10)) # Chai Wah Wu, Feb 16 2024

Crossrefs

Cf. A368366.

Cf. A000045, A000071, A000312, A003266.

Sequence in context: A203533 A015033 A126677 * A054328 A203590 A263056

Adjacent sequences: A370220 A370221 A370222 * A370224 A370225 A370226

Keyword

nonn

Author

Paolo Xausa, Feb 13 2024

Status

approved