A075091 Sum of Lucas numbers and reflected Lucas numbers (comment to A061084).

4, 0, 6, 0, 14, 0, 36, 0, 94, 0, 246, 0, 644, 0, 1686, 0, 4414, 0, 11556, 0, 30254, 0, 79206, 0, 207364, 0, 542886, 0, 1421294, 0, 3720996, 0, 9741694, 0, 25504086, 0, 66770564, 0, 174807606, 0, 457652254, 0, 1198149156, 0, 3136795214, 0, 8212236486, 0, 21499914244, 0

Offset

0,1

Comments

a(n) = ((-1)^n + 1)*L(n), where L(n) denotes the n-th Lucas number.

Links

Table of n, a(n) for n=0..49.

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Formula

a(n) = 3*a(n-2) - a(n-4), a(0)=4, a(1)=0, a(2)=6, a(3)=0.

G.f.: (4 - 6x^2)/(1 - 3*x^2 + x^4).

E.g.f.: 4*cosh(x/2)*cosh(sqrt(5)*x/2). - Stefano Spezia, Aug 30 2025

Mathematica

CoefficientList[Series[(4 - 6*x^2)/(1 - 3*x^2 + x^4), {x, 0, 50}], x]
LinearRecurrence[{0, 3, 0, -1}, {4, 0, 6, 0}, 50] (* or *) Riffle[ LinearRecurrence[ {3, -1}, {4, 6}, 30], 0] (* Harvey P. Dale, Aug 17 2018 *)

Crossrefs

Cf. A000032, A061084.

Sequence in context: A179939 A163407 A023891 * A132953 A387470 A195207

Adjacent sequences: A075088 A075089 A075090 * A075092 A075093 A075094

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 31 2002

Extensions

a(46)-a(49) from Stefano Spezia, Aug 30 2025

Status

approved