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A305412
a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).
2
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
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. 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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 05 2018
STATUS
approved