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A173993 Sequence whose Hankel transform is the Somos (4) sequence. 1
1, 2, 6, 17, 50, 146, 430, 1267, 3746, 11091, 32900, 97716, 290586, 864980, 2577032, 7683397, 22922874, 68427057, 204362172, 610604629, 1825092080, 5457016431, 16321318264, 48828168580, 146112907266, 437319580738, 1309158060068 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A006720(n+3).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

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

Conjecture: (n+1)*a(n) +2*(-4*n-1)*a(n-1) +(19*n-5)*a(n-2) -36*a(n-3) +8*(-7*n+26)*a(n-4) +2*(34*n-143)*a(n-5) +24*(-n+5)*a(n-6)=0. - R. J. Mathar, Oct 10 2014

MATHEMATICA

CoefficientList[Series[(Sqrt[(1-2*x)*(1-2*x-4*x^2+4*x^3)]-2*x^2+4*x-1)/( 2 x*(1 - 4 x + 3 x^2)), {x, 0, 50}], x] (* G. C. Greubel, Sep 22 2018 *)

PROG

(PARI) x='x+O('x^50); Vec((sqrt((1-2x)*(1-2x-4x^2+4x^3))-2x^2+4x-1)/(2x*(1-4x+3x^2))) \\ G. C. Greubel, Sep 22 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((Sqrt((1-2x)*(1-2x-4x^2+4x^3))-2x^2+4x-1)/(2x*(1-4x+3x^2)))); // G. C. Greubel, Sep 22 2018

CROSSREFS

Cf. A173992.

Sequence in context: A244405 A244406 A244407 * A270863 A027914 A098703

Adjacent sequences:  A173990 A173991 A173992 * A173994 A173995 A173996

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 04 2010

STATUS

approved

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)