OFFSET
0,1
LINKS
Robert Israel, Table of n, a(n) for n = 0..19
FORMULA
Conjecture: a(n)=A011455(n-1)+5 where defined. - R. J. Mathar, Apr 26 2007
Proof of conjecture: if d(n) = log_2(a(n+1)-a(n)), we have d(0)=0, d(1)=1, d(n)=d(n-1)+d(n-2), so d(n) = Fibonacci(n). - Robert Israel, Oct 25 2017
EXAMPLE
a(3) = 7, since a(3) = a(2) + [(a(2)-a(1)) * (a(1)-a(0))] = 5 + ((5-3)*(3-2))
MAPLE
f:= proc(n) option remember; procname(n-1)+(procname(n-1)-procname(n-2))*(procname(n-2)-procname(n-3)) end proc:
f(0):= 2: f(1):= 3: f(2):= 5:
map(f, [$0..20]); # Robert Israel, Oct 25 2017
MATHEMATICA
a[0] = 2; a[1] = 3; a[2] = 5; a[n_] := a[n] = a[n - 1] + (a[n - 1] - a[n - 2])*(a[n - 2] - a[n - 3]); Table[a[n], {n, 0, 14}]
PROG
(Magma) I:=[2, 3, 5]; [n le 3 select I[n] else Self(n-1)+(Self(n-1)-Self(n-2))*(Self(n-2)-Self(n-3)): n in [1..15]]; // Vincenzo Librandi, Oct 25 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ajay Chhabra (ajay(AT)cantab.net), Jan 08 2003
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jan 08 2002
Conjecture corrected by Robert Israel, Oct 25 2017
STATUS
approved