A305851 - OEIS

%I #31 Nov 03 2022 13:51:34

%S 1,1,2,9,1331,3224179360000,

%T 348414297354956334043085401797347258376901025074126347562215651

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

%C 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

%H Eric Chen, <a href="/A305851/b305851.txt">Table of n, a(n) for n = 1..9</a>

%H Eric Chen, <a href="/A305851/a305851.txt">Table of n, a(n) for n = 1..10</a> (an a-file)

%F a(n) ~ c^((n-2)!), where c = 3.3203520468282576446980958620234685911457954899308569085994... - _Vaclav Kotesovec_, Jul 23 2018

%t Nest[Append[#, (#[[-1]] + #[[-2]] )^(Length@ # - 2)] &, {1, 1}, 6] (* _Michael De Vlieger_, Jun 11 2018 *)

%t 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 *)

%t 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 *)

%o (Python)

%o #Generates and prints a list containing the terms, up to the term with the index of seq_limit

%o seq_limit=9

%o seq_list=[1,1]

%o for seq_no in range(3,seq_limit):

%o     seq_list.append((seq_list[-1]+seq_list[-2])**(seq_no-2))

%o print(seq_list)

%o (PARI) a(n)=if(n<3,1,(a(n-1)+a(n-2))^(n-2)) \\ _Eric Chen_, Jun 14 2018

%Y Cf. A050923.

%K nonn,easy,less

%O 1,3

%A _Yigithan TAMER_, Jun 11 2018