A193618 G.f. A(x) satisfies: A(x)^2 + A(-x)^2 = 2 and A(x)^-2 - A(-x)^-2 = -8*x.

1, 2, -2, -28, 54, 860, -2004, -33720, 86054, 1492908, -4019452, -71101832, 198310460, 3555617432, -10168382696, -184127171952, 536496907782, 9788598556876, -28937139277804, -531135371147368, 1588378827366868, 29295861148032584

Offset

0,2

Comments

The unsigned version of this sequence, A246062, has g.f.: sqrt( (1 + sqrt(1+8*x)) / (1 + sqrt(1-8*x)) ).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: ( 2*(sqrt(1+64*x^2) + 8*x)/(sqrt(1+64*x^2) + 1) )^(1/4).

G.f. A(x) = 1/G(x) where G(x) is the g.f. of A193619.

Example

G.f.: A(x) = 1 + 2*x - 2*x^2 - 28*x^3 + 54*x^4 + 860*x^5 - 2004*x^6 +...
where
A(x)^2 = 1 + 4*x - 64*x^3 + 2048*x^5 - 81920*x^7 + 3670016*x^9 +...
and
A(x)^-2 = 1 - 4*x + 16*x^2 - 256*x^4 + 8192*x^6 - 327680*x^8 +...

Prog

(PARI) {a(n)=local(Ox=x*O(x^n), A=(2*(sqrt(1+64*x^2+Ox)+8*x)/(sqrt(1+64*x^2+Ox)+1))^(1/4)); polcoeff(A, n)}
(PARI) N=40; x='x+O('x^N); Vec(sqrt(2/(1-8*x+sqrt(1+64*x^2)))) \\ Seiichi Manyama, Aug 26 2020

Crossrefs

Cf. A193619, A246062.

Sequence in context: A121222 A125067 A369755 * A246062 A178955 A012000

Adjacent sequences: A193615 A193616 A193617 * A193619 A193620 A193621

Keyword

sign

Author

Paul D. Hanna, Aug 01 2011

Status

approved