A280931 a(n) = 2*F(n-1) + 9*F(n-4) + 9*F(n-7) where n >= 7 and F = A000045.

34, 62, 96, 158, 254, 412, 666, 1078, 1744, 2822, 4566, 7388, 11954, 19342, 31296, 50638, 81934, 132572, 214506, 347078, 561584, 908662, 1470246, 2378908, 3849154, 6228062, 10077216, 16305278, 26382494, 42687772, 69070266, 111758038, 180828304, 292586342

Offset

7,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 7..1100

H. Zhao and X. Li, On the Fibonacci numbers of trees, The Fibonacci Quarterly, Vol. 44, Number 1 (2006), page 37.

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

Formula

G.f.: 2*x^7*(17 + 14*x)/(1 - x - x^2).

a(n) = a(n-1) + a(n-2).

From the g.f.: a(n) = 34*F(n-6) + 28*F(n-7) = 28*F(n-5) + 6*F(n-6) = 6*F(n-4) + 22*F(n-5) = 22*F(n-3) - 16*F(n-4) = -16*F(n-2) + 38*F(n-3) = 38*F(n-1) - 54*F(n-2) = -54*F(n) + 92*F(n-1), and so on.

a(n) = 2*A022125(n-5).

a(n) = F(n+2) + F(n-3) + F(n-11). - Greg Dresden, Jul 07 2022

Mathematica

LinearRecurrence[{1, 1}, {34, 62}, 35]

Prog

(Magma) [2*Fibonacci(n-1)+9*Fibonacci(n-4)+9*Fibonacci(n-7): n in [7..40]];
(Magma) a0:=34; a1:=62; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]];

Crossrefs

Cf. A000045, A022125, A022130, A101156, A280932.

Sequence in context: A259952 A259945 A303239 * A115159 A125192 A039381

Adjacent sequences: A280928 A280929 A280930 * A280932 A280933 A280934

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 24 2017

Extensions

Corrected and extended by Bruno Berselli, Jan 24 2017

Status

approved