A280932 a(n) = 2*F(n-1) + 2*F(n-3) + 10*F(n-5) + 9*F(n-8) where n >= 8 and F = A000045.

56, 97, 153, 250, 403, 653, 1056, 1709, 2765, 4474, 7239, 11713, 18952, 30665, 49617, 80282, 129899, 210181, 340080, 550261, 890341, 1440602, 2330943, 3771545, 6102488, 9874033, 15976521, 25850554, 41827075, 67677629, 109504704, 177182333, 286687037

Offset: 8

Author

Vincenzo Librandi, Jan 24 2017

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045, A022130, A101156, A280931.

Programs

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]];

Mathematica

LinearRecurrence[{1, 1}, {56, 97}, 35]

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.

Extensions

Corrected and extended by Bruno Berselli, Jan 24 2017