A141752 a(n) = Sum_{k=0..n} ( Fibonacci(2*k-1) + (n-k)*Fibonacci(2*k) ).

1, 2, 5, 14, 39, 106, 283, 748, 1967, 5160, 13521, 35412, 92725, 242774, 635609, 1664066, 4356603, 11405758, 29860687, 78176320, 204668291, 535828572, 1402817445, 3672623784, 9615053929, 25172538026, 65902560173, 172535142518

Offset: 0

Author

Paul D. Hanna, Jul 04 2008

Keywords

• nonn
• easy

Comments

Row sums of triangle A141751.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-8,5,-1).

Crossrefs

Cf. A054452, A055588, A141751.

Programs

Mathematica

LinearRecurrence[{5,-8,5,-1},{1,2,5,14},30] (* Harvey P. Dale, May 23 2021 *)

PARI

a(n)=sum(k=0,n,fibonacci(2*k-1) + (n-k)*fibonacci(2*k))

Formula

G.f.: (1 - 3*x + 3*x^2)/((1 - 3*x + x^2)*(1-x)^2).

a(n) = A055588(n) + A054452(n). - R. J. Mathar, Apr 16 2016

a(n) = 5*a(n-1)-8*a(n-2)+5*a(n-3)-a(n-4). - Wesley Ivan Hurt, Oct 18 2021