A168494 Sequence with Hankel transform equal to 3^floor(n^2/3).

1, 1, 2, 7, 32, 160, 830, 4405, 23798, 130498, 724748, 4069258, 23064608, 131809108, 758696492, 4394825647, 25600773272, 149877922228, 881394158558, 5204245242208, 30841413359186, 183381577399006, 1093695670905206

Offset

0,3

Comments

Hankel transform is A168495.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

G.f.: 1/(1-x/(1-x/(1-3x/(1-x/(1-x/(1-3x/(1-x/(1-x/(1-3x/(1-.... (continued fraction);

G.f.: 1/(1-x-x^2/(1-4x-3x^2/(1-2x-3x^2/(1-4x-x^2/(1-4x-3x^2/(1-2x-3x^2/(1-4x-x^2/(1-... (continued fraction),

with sequences (1,3,3,1,3,3,1,3,3,1,...) and (1,4,2,4,4,2,4,4,2,4,4,...).

G.f.: (1+x-sqrt(1-10x+25x^2-12x^3))/(6x(1-x)).

a(n) = Sum_{k=0..n} A091866(n,k)*3^(n-k). - Philippe Deléham, Nov 27 2009

Conjecture: (n+1)*a(n) +(4-11*n)*a(n-2) +5*(7*n-11)*a(n-2) +(92-37*n) * a(n-3) +6*(2*n-7)*a(n-4) = 0. - R. J. Mathar, Sep 30 2012

a(n) ~ sqrt(33-sqrt(33))*((7+sqrt(33))/2)^n/(12*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012

Mathematica

CoefficientList[Series[(1+x-Sqrt[1-10*x+25*x^2-12*x^3])/(6*x*(1-x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)

Crossrefs

Cf. A000108, A091866, A109033. - Philippe Deléham, Nov 27 2009

Sequence in context: A334854 A047850 A201373 * A181376 A183951 A226994

Adjacent sequences: A168491 A168492 A168493 * A168495 A168496 A168497

Keyword

easy,nonn

Author

Paul Barry, Nov 27 2009

Status

approved