A080042 a(n) = 4*a(n-1)+3*a(n-2) for n>1, a(0)=2, a(1)=4.

2, 4, 22, 100, 466, 2164, 10054, 46708, 216994, 1008100, 4683382, 21757828, 101081458, 469599316, 2181641638, 10135364500, 47086382914, 218751625156, 1016265649366, 4721317472932, 21934066839826, 101900219778100

Offset

0,1

Comments

This is the Lucas sequence V(4,-3). [Bruno Berselli, Jan 09 2013]

Links

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

Wikipedia, Lucas sequence: Specific names.

Index entries for linear recurrences with constant coefficients, signature (4, 3).

Formula

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

a(n) = (2+sqrt(7))^n+(2-sqrt(7))^n.

G.f.: G(0)/x -2/x, where G(k)= 1 + 1/(1 - x*(7*k-4)/(x*(7*k+3) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013

a(n) = [x^n] ( (1 + 4*x + sqrt(1 + 8*x + 28*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015

Mathematica

CoefficientList[Series[(2 - 4 t)/(1 - 4 t - 3 t^2), {t, 0, 25}], t]

Prog

(Sage) [lucas_number2(n, 4, -3) for n in range(0, 22)] # Zerinvary Lajos, May 14 2009

Crossrefs

Cf. A015530: Lucas sequence U(4,-3).

Sequence in context: A071298 A152104 A047035 * A364643 A324145 A366732

Adjacent sequences: A080039 A080040 A080041 * A080043 A080044 A080045

Keyword

nonn,easy

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003

Status

approved