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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
OFFSET
0,1
LINKS
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
Sequence in context: A152752 A095344 A141635 * A371374 A339324 A145971
KEYWORD
nonn,easy
EXTENSIONS
Name corrected by Colin Barker, Apr 24 2015
STATUS
approved