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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214761 G.f. satisfies: A(x) = 1/A(-x*A(x)). 8
1, 2, 4, 12, 40, 128, 416, 1344, 4224, 12928, 38016, 104832, 260096, 512256, 329728, -4140032, -33444864, -184423424, -883798016, -3935711232, -16759001088, -69266997248, -280327684096, -1116872122368, -4394989174784, -17112512544768, -65974620848128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare g.f. to: G(x) = 1/G(-x*G(x)) when G(x) = 1/(1-x).

An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)); for example, (*) is satisfied by G(x) = 1/(1-m*x).

LINKS

Table of n, a(n) for n=0..26.

FORMULA

The g.f. of this sequence is the limit of the recurrence:

(*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)))/2 starting at G_0(x) = 1+2*x.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 40*x^4 + 128*x^5 + 416*x^6 + 1344*x^7 +...

Related expansions:

1/A(x) = A(-x*A(x)) = 1 - 2*x - 4*x^3 - 8*x^4 - 16*x^5 - 48*x^6 - 96*x^7 - 128*x^8 + 64*x^9 + 2048*x^10 +...

PROG

(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^1+x*O(x^n)))/2); polcoeff(A, n)}

for(n=0, 31, print1(a(n), ", "))

CROSSREFS

Cf. A214762, A214763, A214764, A214765, A214766, A214767, A214768, A214769.

Sequence in context: A099214 A126946 A113179 * A327845 A056236 A300652

Adjacent sequences:  A214758 A214759 A214760 * A214762 A214763 A214764

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jul 29 2012

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 December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)