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).

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

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 * A371374 A339324 A145971

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