A305412 a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).

1, 3, 5, 11, 23, 53, 125, 307, 769, 1959, 5039, 13049, 33929, 88451, 230957, 603667, 1578823, 4130829, 10810469, 28295411, 74067401, 193893263, 507590495, 1328842801, 3478880593, 9107706243, 23844088085, 62424315227, 163428464759, 427860443429, 1120151837069

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

Formula

G.f.: (1 - 5*x^2 - 2*x^3 + x^4)/((x + 1)*(1 - 3*x + x^2)*(1 - x - x^2)).

a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5).

5*a(n) = (-1)^(n+1) +5*F(n+2) + A002878(n). - R. J. Mathar, Nov 14 2019

Mathematica

Table[Fibonacci[n] Fibonacci[n+1] + Fibonacci[n+2], {n, 0, 30}]

Prog

(Magma) [Fibonacci(n)*Fibonacci(n+1)+Fibonacci(n+2): n in [0..30]];
(GAP) List([0..35], n -> Fibonacci(n)*Fibonacci(n+1)+Fibonacci(n+2)); # Muniru A Asiru, Jun 06 2018

Crossrefs

Cf. A001654, A269803.

Cf. A059769: F(n)*F(n+1) - F(n+2), with offset 3.

Equals A000045 + A286983.

First differences are listed in A059727 (after 0).

Sequence in context: A037446 A113151 A269964 * A094810 A139376 A074892

Adjacent sequences: A305409 A305410 A305411 * A305413 A305414 A305415

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 05 2018

Status

approved