A168492 Sequence with Hankel transform equal to 3^floor(n^2/2).

1, 1, 2, 7, 38, 250, 1748, 12463, 89606, 647710, 4702844, 34286038, 250928732, 1843209556, 13586564072, 100479347647, 745418148806, 5546324817718, 41382983725292, 309586136922898, 2321772733668980, 17453199438926188, 131489046194284568, 992678648890643206

Offset

0,3

Comments

Hankel transform is A168493 (a trivial Somos-4 sequence linked to y^2=1-16x+76x^2-96x^3).

Links

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

Formula

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

G.f.: 1/(1-x-x^2/(1-4x-9x^2/(1-4x-x^2/(1-4x-9x^2/(1-4x-x^2/(1-4x-9x^2/(1-... (continued fraction);

G.f.: (1-2*x-sqrt((1-2*x)*(1-14*x+48*x^2)))/(6*x*(1-2*x)).

Recurrence: (n+1)*a(n) = 2*(8*n-3)*a(n-1) - 4*(19*n-31)*a(n-2) + 48*(2*n-5)* a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 2^(3*n+1)/(3*sqrt(3*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012

a(n) = Sum_{k, 0<=k<=n} A168511(n,k)*3^(n-k). - Philippe Deléham, Mar 19 2013

Mathematica

CoefficientList[Series[(1-2*x-Sqrt[(1-2*x)(1-14*x+48*x^2)])/(6*x*(1-2*x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Crossrefs

Sequence in context: A094431 A256032 A209006 * A346646 A032109 A368232

Adjacent sequences: A168489 A168490 A168491 * A168493 A168494 A168495

Keyword

easy,nonn

Author

Paul Barry, Nov 27 2009

Status

approved