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.
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
KEYWORD
nonn,easy,changed
AUTHOR
James M. Saker, Dec 17 2017
STATUS
approved