OFFSET
0,3
COMMENTS
This is a recurrence relation which has 1,1 and 2 as the base cases and the n-th term is obtained by multiplying the (n-2)th term by 2 and adding it with the product of (n-1)th and (n-3)rd term.
FORMULA
a(n) ~ c^(d^n), where d = 1.465571231876768026... is the root of the equation d^3 = d^2 + 1 and c = 1.604048928929157460568... . - Vaclav Kotesovec, Oct 01 2015
MAPLE
f:=proc(n) option remember;
if n <= 1 then 1 elif n=2 then 2 else
f(n-1)*f(n-3)+2*f(n-2); fi; end;
[seq(f(n), n=0..15)]; # N. J. A. Sloane, Oct 01 2015
MATHEMATICA
RecurrenceTable[{a[0]==a[1]==1, a[2]==2, a[n]==2a[n-2]+a[n-1]a[n-3]}, a, {n, 20}] (* Harvey P. Dale, Oct 01 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mohit Maheshwari (mohitmahe1989(AT)gmail.com), Jan 19 2008
EXTENSIONS
Corrected by Harvey P. Dale, Oct 01 2015
STATUS
approved