login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111235 a(1)=a(2)=a(3)=a(4)=1. For n >= 5, a(n)= a(n-1)*a(n-2) + a(n-3)*a(n-4). 2
1, 1, 1, 1, 2, 3, 7, 23, 167, 3862, 645115, 2491437971, 1607264007306619, 4004398577225334507664179, 6436125704084114770053956998574742562466, 25772812612277833490303309040566300172816894832780792086674335463 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(5*n) is always even. Every other term of the sequence is odd.

It is easy to see that a(n) >= A000301(n-3) for all n. From that we can deduce that a(n) >= 2^(Fibonacci(n-3)). Can anybody give a formula for the asymptotic behavior? - Stefan Steinerberger, Jan 21 2006

As n->infinity, log(a(n))/phi^n approaches t-(-1)^n*u/phi^(2*n), where phi=(1+sqrt(5))/2, t=0.0672009781433377128..., and u=0.766475715574332057.... - Jon E. Schoenfield, Sep 14 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..21

MAPLE

a:= proc(n) a(n):= `if`(n<5, 1, a(n-1)*a(n-2) +a(n-3)*a(n-4)) end:

seq(a(n), n=1..16);  # Alois P. Heinz, Mar 30 2014

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==a[n-1]a[n-2]+a[n-3] a[n-4]}, a, {n, 20}] (* Harvey P. Dale, Jun 06 2017 *)

PROG

(MAGMA) I:=[1, 1, 1, 1]; [n le 4 select I[n] else Self(n-1)*Self(n-2) +Self(n-3)*Self(n-4): n in [1..16]]; // Vincenzo Librandi, Mar 30 2014

CROSSREFS

Cf. A239967.

Sequence in context: A090253 A001064 A108176 * A066356 A006892 A296397

Adjacent sequences:  A111232 A111233 A111234 * A111236 A111237 A111238

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, Oct 28 2005

EXTENSIONS

More terms from Stefan Steinerberger, Jan 21 2006

More terms from Joshua Zucker, May 04 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 01:20 EDT 2020. Contains 337235 sequences. (Running on oeis4.)