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!)
A177117 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)=4, k=-2 and l=0. 1
1, 4, 4, 18, 60, 270, 1152, 5254, 24028, 112606, 533320, 2559974, 12404900, 60657566, 298826672, 1482082774, 7393735948, 37078771678, 186813107800, 945165976262, 4800095713844, 24461416209374, 125046320212160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

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=-2, l=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +3*(n+1)*a(n-2) +3*(13*n-44)*a(n-3) +2*(-28*n+113)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

EXAMPLE

a(2)=2*1*4-4=4. a(3)=2*1*4-4+4^2-2=18. a(4)=2*1*18-4+2*4*4-4=60.

MAPLE

l:=0: : k := -2 : m:=4: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. A177115.

Sequence in context: A214187 A214238 A133039 * A272321 A272290 A271688

Adjacent sequences:  A177114 A177115 A177116 * A177118 A177119 A177120

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, May 03 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 22:57 EST 2020. Contains 332216 sequences. (Running on oeis4.)