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A215042 a(n) = F(8*n)/L(2*n) with n >= 0, F = A000045 (Fibonacci numbers) and L = A000032 (Lucas numbers). 1
0, 7, 141, 2576, 46347, 831985, 14930208, 267913919, 4807525989, 86267568688, 1548008749155, 27777890017577, 498454011832896, 8944394323670071, 160500643816049277, 2880067194369984080, 51680708854856144763, 927372692193073296289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This provides the second example for the Riordan transition matrix R mentioned in a comment to A078812 (here the column called there n=1 is relevant).

LINKS

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (21,-56,21,-1).

FORMULA

a(n) = 2*F(2*n) + 1*5*F(2*n)^3, n >= 0 (for the coefficients 2, 1,  see the second row of the Riordan matrix R = A078812 (with offset [0,0])).

a(n) = F(6*n) - F(2*n), n >= 0, (from the preceding line and a 5*F(2*n)^3 formula given in a comment on the signed triangle A111418, with l->2*n, n->1; see also 5*A215039).

O.g.f.: x*(7-6*x+7*x^2)/((1-3*x+x^2)*(1-18*x+x^2)). The partial fraction decomposition and recurrences lead to the preceding formula.

MATHEMATICA

Table[Fibonacci[8 n]/LucasL[2 n], {n, 0, 17}] (* Bruno Berselli, Aug 31 2012 *)

PROG

(MAGMA) [Fibonacci(8*n)/Lucas(2*n): n in [0..17]]; // Bruno Berselli, Aug 31 2012

CROSSREFS

Cf. A001906 (for F(4*n)/L(2*n) = F(2*n)), 24*A215043 (for F(12*n)/L(2*n)).

Sequence in context: A306628 A302912 A191956 * A221267 A070074 A051397

Adjacent sequences:  A215039 A215040 A215041 * A215043 A215044 A215045

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2012

STATUS

approved

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Last modified March 25 10:19 EDT 2019. Contains 321470 sequences. (Running on oeis4.)