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A014717 a(n) = (F(n+1) + L(n))^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032). 1
9, 4, 25, 49, 144, 361, 961, 2500, 6561, 17161, 44944, 117649, 308025, 806404, 2111209, 5527201, 14470416, 37884025, 99181681, 259660996, 679801329, 1779742969, 4659427600, 12198539809, 31936191849, 83610035716, 218893915321, 573071710225, 1500321215376 (list; graph; refs; listen; history; text; internal format)
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*a(n-1) + 2*a(n-2) - a(n-3). - Colin Barker, Apr 23 2015

G.f.: (9 - 14*x - x^2)/ ((1+x)*(1-3*x+x^2)). - Colin Barker, Apr 23 2015

a(n) = A013655(n)^2. - Hartmut F. W. Hoft, Apr 24 2015

a(n) = (1/5)*(22*(-1)^n + 19*Fibonacci(2*n) + 23*Fibonacci(2*n-1)). - Ehren Metcalfe, Mar 26 2016

a(n) = (2^(-1-n)*(11*(-1)^n*2^(2+n) + (23-3*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(23+3*sqrt(5))))/5. - Colin Barker, Oct 01 2016

a(n) = 3*a(n-1) - a(n-2) + 22*(-1)^n. - Greg Dresden, May 18 2020

MATHEMATICA

Table[(Fibonacci[n+1] + LucasL[n])^2, {n, 0, 30}] (* Michael De Vlieger, Apr 24 2015 *)

PROG

(PARI) lucas(n) = if(n==0, 2, fibonacci(2*n)/fibonacci(n))

a(n) = (fibonacci(n+1)+lucas(n))^2 \\ Colin Barker, Apr 24 2015

(PARI) Vec( (9-14*x-x^2)/((1+x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, Apr 23 2015

(PARI) a(n) = (2*fibonacci(n+1)+fibonacci(n-1))^2

(MAGMA) [(Fibonacci(n+1) + Lucas(n))^2: n in [0..30]]; // Vincenzo Librandi, Apr 25 2015

CROSSREFS

Cf. A000032, A000045, A013655.

Sequence in context: A174679 A168077 A173536 * A104728 A058093 A164032

Adjacent sequences:  A014714 A014715 A014716 * A014718 A014719 A014720

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

Name corrected by Colin Barker, Apr 24 2015

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)