A075150 a(n)=L(n)*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (see comment to A061084).

4, -1, 9, -16, 49, -121, 324, -841, 2209, -5776, 15129, -39601, 103684, -271441, 710649, -1860496, 4870849, -12752041, 33385284, -87403801, 228826129, -599074576, 1568397609, -4106118241, 10749957124, -28143753121, 73681302249, -192900153616, 505019158609, -1322157322201

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-2,2,1).

Formula

a(n) = 2+(-1)^n*L(2n).

a(n) = -2a(n-1)+2a(n-2)+a(n-3) with a(0)=4, a(1)=-1, a(2)=9.

G.f.: (4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3).

a(n) = (-1)^n*A001254(n). - R. J. Mathar, Jan 11 2012

a(n) = (2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n). - Colin Barker, Oct 01 2016

Mathematica

CoefficientList[Series[(4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3), {x, 0, 30}], x]
LinearRecurrence[{-2, 2, 1}, {4, -1, 9}, 50] (* Harvey P. Dale, Nov 08 2011 *)

Prog

(PARI) a(n) = round((2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n)) \\ Colin Barker, Oct 01 2016
(PARI) Vec((4+7*x-x^2)/(1+2*x-2*x^2-x^3) + O(x^30)) \\ Colin Barker, Oct 01 2016

Crossrefs

Cf. A000032, A061084.

Sequence in context: A344109 A193580 A244761 * A001254 A143763 A278350

Adjacent sequences: A075147 A075148 A075149 * A075151 A075152 A075153

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002

Status

approved