OFFSET
8,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 8..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.: x^8*(56 + 41*x)/(1 - x - x^2).
a(n) = a(n-1) + a(n-2).
From the g.f.: a(n) = 56*F(n-7) + 41*F(n-8) = 41*F(n-6) + 15*F(n-7) = 15*F(n-5) + 26*F(n-6) = 26*F(n-4) - 11*F(n-5) = -11*F(n-3) + 37*F(n-4) = 37*F(n-2) - 48*F(n-3) = -48*F(n-1) + 85*F(n-2) = 85*F(n) - 133*F(n-1), and so on.
MATHEMATICA
LinearRecurrence[{1, 1}, {56, 97}, 35]
PROG
(Magma) [2*Fibonacci(n-1)+2*Fibonacci(n-3)+10*Fibonacci(n-5)+9*Fibonacci(n-8): n in [8..40]];
(Magma) a0:=56; a1:=97; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 24 2017
EXTENSIONS
Corrected and extended by Bruno Berselli, Jan 24 2017
STATUS
approved