login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177171 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=9, k=0 and l=-2. 1
1, 9, 16, 111, 508, 3268, 19230, 125859, 815208, 5494796, 37280170, 257711524, 1796835778, 12665947790, 89949355454, 643580501287, 4632487753748, 33531130466872, 243877573413062, 1781555056684620, 13065400778105878 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=0, l=-2).
Conjecture: +(n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-23*n+51)*a(n-2) +2*(34*n-105)*a(n-3) +40*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016
EXAMPLE
a(2)=2*1*9-2=16. a(3)=2*1*16+81-2=111.
MAPLE
l:=-2: : k := 0 : m:=9:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);
CROSSREFS
Cf. A177170.
Sequence in context: A179307 A014720 A138238 * A226232 A267088 A204268
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, May 04 2010
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)