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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158122 G.f. A(x) satisfies: A(x)^2 = 1/AGM(1, 1 - 8*x/A(x)^2 ). 5
1, 2, 0, 0, 2, -4, 0, 0, -16, 40, 0, 0, 200, -544, 0, 0, -3006, 8540, 0, 0, 49956, -145720, 0, 0, -884352, 2625648, 0, 0, 16349648, -49161024, 0, 0, -311986480, 947069352, 0, 0, 6098614912, -18650752400, 0, 0, -121497078016, 373773754912, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean.

LINKS

Table of n, a(n) for n=0..43.

FORMULA

G.f.: A(x) = sqrt( x/Series_Reversion( x/AGM(1,1-8*x) ) ).

Self-convolution equals A158100.

Contribution from Paul D. Hanna, Mar 14 2009: (Start)

Quadrasections are A158212(n) = A158122(4n) and A158213 = A158122(4n+1);

let B(x), C(x), be the g.f.s of A158212 and A158213, respectively,

then C(x) = 2/B(x) so that

A(x) = B(x^4) + x*C(x^4) = B(x^4) + 2*x/B(x^4) = 2/C(x^4) + x*C(x^4). (End)

EXAMPLE

G.f.: A(x) = 1 + 2*x + 2*x^4 - 4*x^5 - 16*x^8 + 40*x^9 + 200*x^12 -+...

A(x)^2 = 1 + 4*x + 4*x^2 + 4*x^4 - 16*x^6 - 28*x^8 + 176*x^10 +...

Contribution from Paul D. Hanna, Mar 14 2009: (Start)

G.f. of quadrasection A158212 is:

B(x) = 1 + 2*x - 16*x^2 + 200*x^3 - 3006*x^4 + 49956*x^5 +...;

G.f. of quadrasection A158213 is C(x) = 2/B(x):

C(x) = 2 - 4*x + 40*x^2 - 544*x^3 + 8540*x^4 - 145720*x^5 +...

where g.f. A(x) = B(x^4) + x*C(x^4) = B(x^4) + 2*x/B(x^4). (End)

PROG

(PARI) {a(n)=polcoeff(sqrt(x/serreverse(x/agm(1, 1-8*x +x*O(x^n)))), n)}

CROSSREFS

Cf. A060691, A158100 (self-convolution), A258053.

Cf. quadrasections: A158212, A158213.

Sequence in context: A020474 A135589 A244312 * A028641 A325190 A141416

Adjacent sequences:  A158119 A158120 A158121 * A158123 A158124 A158125

KEYWORD

sign

AUTHOR

Paul D. Hanna, Mar 13 2009

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 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)