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A091565 Expansion of (1 - x - sqrt(1 - 2*x + x^2 - 8*x^3)) / (4*x^2) in powers of x. 0
0, 1, 1, 1, 3, 7, 13, 29, 71, 163, 377, 913, 2219, 5375, 13189, 32677, 81167, 202523, 508273, 1280537, 3236275, 8207543, 20880893, 53263405, 136205527, 349137811, 896881641, 2308523809, 5953138875, 15378562415, 39791453685, 103115768885 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Series reversion of g.f. A(x) is -A(-x).

LINKS

Table of n, a(n) for n=0..31.

Paul Barry, Riordan Pseudo-Involutions, Continued Fractions and Somos 4 Sequences, arXiv:1807.05794 [math.CO], 2018.

FORMULA

G.f.: (1 - x - sqrt(1 - 2*x + x^2 - 8*x^3)) / (4*x^2) = 2*x / (1 - x + sqrt(1 - 2*x + x^2 - 8*x^3))  .

G.f. A(x) = y satisfies 2*(x*y)^2 + (x - 1)*y + x = 0.

a(n) = a(n-1) + 2*(a(1)*a(n-3) + a(2)*a(n-4) + ... + a(n-3)*a(1)) for n>1.

D-finite with recurrence: +(n+2)*a(n) +(-2*n-1)*a(n-1) +(n-1)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

EXAMPLE

x + x^2 + x^3 + 3*x^4 + 7*x^5 + 13*x^6 + 29*x^7 + 71*x^8 + 163*x^9 + ...

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( 2 * x / (1 - x + sqrt(1 - 2*x + x^2 - 8*x^3 + x * O(x^n))), n))}

CROSSREFS

Cf. A025249.

Sequence in context: A283323 A260022 A134270 * A025249 A147098 A109291

Adjacent sequences:  A091562 A091563 A091564 * A091566 A091567 A091568

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 21 2004

STATUS

approved

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Last modified May 27 06:28 EDT 2020. Contains 334649 sequences. (Running on oeis4.)