OFFSET
1,1
COMMENTS
The calculations for the first few values of the sequence are
... 2^3 = 8 so a(3) = 18/1 = 18
... 18^3 = 5832 so a(4) = 583218/18 = 32401
... 32401^3 = 34015373377201 so a(5) = 34015373377201583218/32401 = 1049824801000018.
FORMULA
DEFINITION
a(1) = 2, a(2) = 1, and for n >= 3,
(1)... a(n) = concatenate (a(n-1)^3,a(n-2)^3,...,a(1)^3)/a(n-1).
RECURRENCE RELATION
It appears that for n >= 2,
(2)... a(n+2) = 100^F(n-1,3)*a(n+1)^2 + a(n)
= 100^A006190(n-1)*a(n+1)^2 + a(n)
= 10^A052991(n-1)*a(n+1)^2 + a(n),
where F(n,3) is the n-th Fibonacci polynomial F(n,x) evaluated at x = 3.
EXAMPLE
a(7) = 12 14695 19405 33697 08585 73749 64887 08343 06977 30753 71161 37983 82152 46308 85158 49299 58480 00000 00001 04982 48010 00000 00000 00000 00000 00000 00000 00000 00000 00000 00001 04982 48010 00018 has 167 digits.
MAPLE
M:=6: a:=array(1..M):s:=array(1..M):
a[1]:=2: a[2]:=1:
s[1]:=convert(a[1]^3, string): s[2]:=cat(convert(a[2]^3, string), s[1]):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(convert(a[n]^3, string), s[n-1]);
end do:
seq(a[n], n = 1..M);
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Peter Bala, Dec 09 2010
STATUS
approved