A296654 a(n) = a(n-1)^(n-1) + a(n-2)^(n-1) with a(0)=0 and a(1)=1.

0, 1, 1, 2, 9, 6577, 12306631859123175706, 3474043529146829488927111861423483193112729272713962664092676147662131025218002457407344065137809384265569709358945

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..7.

Example

For n=2, a(2) = 1^(2-1) + 0^(2-1) = 1^1 + 0^1 = 1;
for n=3, a(3) = 1^(3-1) + 1^(3-1) = 1^2 + 1^2 = 2.

Mathematica

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

Prog

(PARI) a(n) = if (n<=1, n, a(n-1)^(n-1) + a(n-2)^(n-1)); \\ Michel Marcus, Dec 28 2017

Crossrefs

Cf. A175980.

Sequence in context: A208214 A280256 A175980 * A027734 A328201 A028581

Adjacent sequences: A296651 A296652 A296653 * A296655 A296656 A296657

Keyword

nonn,easy

Author

James M. Saker, Dec 17 2017

Status

approved