login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014718 a(n) = (F(n+1)+L(n)+n)^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032). 1
9, 9, 49, 100, 256, 576, 1369, 3249, 7921, 19600, 49284, 125316, 321489, 829921, 2152089, 5597956, 14592400, 38093584, 99540529, 260273689, 680844649, 1781515264, 4662431524, 12203620900, 31944770361, 83624494041, 218918244769, 573112589764, 1500389809216 (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 (7,-16,7,23,-28,-3,17,-4,-3,1).

FORMULA

G.f.: -(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2). - Colin Barker, Apr 24 2015

MATHEMATICA

Table[(Fibonacci[n+1]+LucasL[n]+n)^2, {n, 0, 50}] (* or *) LinearRecurrence[ {7, -16, 7, 23, -28, -3, 17, -4, -3, 1}, {9, 9, 49, 100, 256, 576, 1369, 3249, 7921, 19600}, 50] (* Harvey P. Dale, Oct 04 2017 *)

PROG

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

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

(PARI) Vec(-(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2) + O(x^100)) \\ Colin Barker, Apr 24 2015

(PARI) a(n)=(fibonacci(n-1)+2*fibonacci(n+1)+n)^2 \\ Charles R Greathouse IV, Apr 24 2015

CROSSREFS

Cf. A000032, A000045.

Sequence in context: A152752 A095344 A141635 * A339324 A145971 A241868

Adjacent sequences:  A014715 A014716 A014717 * A014719 A014720 A014721

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

Name corrected by Colin Barker, Apr 24 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 14:00 EDT 2021. Contains 343154 sequences. (Running on oeis4.)