A305851 a(n) = (a(n-1)+a(n-2))^(n-2) with a(1)=a(2)=1.

1, 1, 2, 9, 1331, 3224179360000, 348414297354956334043085401797347258376901025074126347562215651

Offset

1,3

Comments

a(8) has 376 digits, a(9) has 2627 digits, a(10) has 21015 digits, see b-file and a-file. - Eric Chen, Jun 14 2018

Links

Eric Chen, Table of n, a(n) for n = 1..9

Eric Chen, Table of n, a(n) for n = 1..10 (an a-file)

Formula

a(n) ~ c^((n-2)!), where c = 3.3203520468282576446980958620234685911457954899308569085994... - Vaclav Kotesovec, Jul 23 2018

Mathematica

Nest[Append[#, (#[[-1]] + #[[-2]] )^(Length@ # - 2)] &, {1, 1}, 6] (* Michael De Vlieger, Jun 11 2018 *)
RecurrenceTable[{a[n] == (a[n-1] + a[n-2])^(n-2), a[1] == 1, a[2] == 1}, a, {n, 1, 7}] (* Vaclav Kotesovec, Jul 23 2018 *)
nxt[{n_, a_, b_}]:={n+1, b, (a+b)^(n-1)}; NestList[nxt, {1, 1, 1}, 7][[All, 2]] (* Harvey P. Dale, Nov 03 2022 *)

Prog

(Python)
#Generates and prints a list containing the terms, up to the term with the index of seq_limit
seq_limit=9
seq_list=[1, 1]
for seq_no in range(3, seq_limit):
    seq_list.append((seq_list[-1]+seq_list[-2])**(seq_no-2))
print(seq_list)
(PARI) a(n)=if(n<3, 1, (a(n-1)+a(n-2))^(n-2)) \\ Eric Chen, Jun 14 2018

Crossrefs

Cf. A050923.

Sequence in context: A062840 A024226 A252584 * A208207 A229050 A221177

Adjacent sequences: A305848 A305849 A305850 * A305852 A305853 A305854

Keyword

nonn,easy,less

Author

Yigithan TAMER, Jun 11 2018

Status

approved