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a(n) = a(n-1)^(n-1) + a(n-2)^(n-1) with a(0)=0 and a(1)=1.
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%I #24 Nov 24 2024 00:05:11

%S 0,1,1,2,9,6577,12306631859123175706,

%T 3474043529146829488927111861423483193112729272713962664092676147662131025218002457407344065137809384265569709358945

%N a(n) = a(n-1)^(n-1) + a(n-2)^(n-1) with a(0)=0 and a(1)=1.

%C It appears as though the logarithm of the logarithm of each term i.e. log(log(a(n))) forms a linear curve; albeit there is little evidence to substantiate that this observation holds.

%e For n=2, a(2) = 1^(2-1) + 0^(2-1) = 1^1 + 0^1 = 1;

%e for n=3, a(3) = 1^(3-1) + 1^(3-1) = 1^2 + 1^2 = 2.

%t RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == a[n - 1]^(n - 1) + a[n - 2]^(n - 1)}, a, {n, 0, 8}] (* _Bruno Berselli_, Dec 28 2017 *)

%t Fold[Append[#1, #1[[#2 + 1]]^(#2) + #1[[#2]]^(#2)] &, {0, 1}, Range@ 6] (* _Michael De Vlieger_, Jan 14 2018 *)

%t nxt[{n_,a_,b_}]:={n+1,b,a^n+b^n}; NestList[nxt,{1,0,1},7][[All, 2]] (* _Harvey P. Dale_, Sep 30 2019 *)

%o (PARI) a(n) = if (n<=1, n, a(n-1)^(n-1) + a(n-2)^(n-1)); \\ _Michel Marcus_, Dec 28 2017

%Y Cf. A175980.

%K nonn,easy

%O 0,4

%A _James M. Saker_, Dec 17 2017