A173993 Sequence whose Hankel transform is the Somos (4) sequence.

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

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