A134455 a(0) = a(1) = 1, a(2) = 2; a(n) = 2*a(n-2) + a(n-1)*a(n-3).

1, 1, 2, 4, 8, 24, 112, 944, 22880, 2564448, 2420884672, 55389846424256, 142044380887832220032, 343873064435082883562892998016, 19047076228497528742755382412205052966716160

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.

Links

Table of n, a(n) for n=0..14.

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

Sequence in context: A002908 A004528 A066535 * A191700 A000643 A261489

Adjacent sequences: A134452 A134453 A134454 * A134456 A134457 A134458

Keyword

easy,nonn

Author

Mohit Maheshwari (mohitmahe1989(AT)gmail.com), Jan 19 2008

Extensions

Corrected by Harvey P. Dale, Oct 01 2015

Status

approved