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A168503 Expansion of 1/(1-x/(1-2x/(1-3x/(1-x/(1-2x/(1-3x/(1-... (continued fraction). 1
1, 1, 3, 15, 87, 531, 3339, 21483, 140859, 938331, 6334875, 43257483, 298276587, 2074128363, 14529077163, 102432060459, 726280074027, 5175707802795, 37051160719275, 266319772644267, 1921345252699563, 13907901060055467 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A168504. First column of array whose production matrix begins

1, 1,

2, 5, 1,

0, 3, 3, 1,

0, 0, 6, 4, 1,

0, 0, 0, 2, 5, 1,

0, 0, 0, 0, 3, 3, 1

0, 0, 0, 0, 0, 6, 4, 1

LINKS

Table of n, a(n) for n=0..21.

FORMULA

G.f.: 1/(1-x-2x^2/(1-5x-3x^2/(1-3x-6x^2/(1-4x-2x^2/(1-5x-3x^2/(1-3x-6x^2/(1-... (continued fraction, defined by the sequences (1,5,3,4,5,3,4,5,3,4,....) and (2,3,6,2,3,6,2,3,6,...);

G.f.: (1-sqrt(1-12*x+36*x^2-24*x^3))/(6*x*(1-x)).

G.f.: (2*x-1)/(Q(0)-3*x), where Q(k) = 6*x - 1 -  6*x^3/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 26 2013

Conjecture: (n+1)*a(n) +(-13*n+5)*a(n-1) +6*(8*n-13)*a(n-2) +12*(-5*n+13)*a(n-3) +12*(2*n-7)*a(n-4)=0. - R. J. Mathar, Feb 10 2015

MATHEMATICA

Join[{1}, Table[SeriesCoefficient[Series[1/(1+ContinuedFractionK[(Mod[k-1, 3]+1)*x*-1, 1, {k, 1, 50}]), {x, 0, 50}], n], {n, 1, 50}]] (* Benedict W. J. Irwin, Feb 07 2016 *)

CROSSREFS

Sequence in context: A075841 A152596 A278392 * A089022 A246538 A132371

Adjacent sequences:  A168500 A168501 A168502 * A168504 A168505 A168506

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 27 2009

STATUS

approved

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)