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
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).
Programs
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Magma
[2*Fibonacci(n-1)+9*Fibonacci(n-4)+9*Fibonacci(n-7): n in [7..40]];
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Magma
a0:=34; a1:=62; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]];
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Mathematica
LinearRecurrence[{1, 1}, {34, 62}, 35]
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
Extensions
Corrected and extended by Bruno Berselli, Jan 24 2017