A206420 Fibonacci sequence beginning 11, 8.

11, 8, 19, 27, 46, 73, 119, 192, 311, 503, 814, 1317, 2131, 3448, 5579, 9027, 14606, 23633, 38239, 61872, 100111, 161983, 262094, 424077, 686171, 1110248, 1796419, 2906667, 4703086, 7609753, 12312839, 19922592, 32235431, 52158023, 84393454, 136551477

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000045.

Programs

Magma

I:=[11, 8]; [n le 2 select I[n] else Self(n-1)+ Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 18 2012

Mathematica

LinearRecurrence[{1, 1}, {11, 8}, 60]

PARI

Vec((11 - 3*x)/(1 - x - x^2) + O(x^30)) \\ Andrew Howroyd, Aug 28 2018

Python

def aupton(terms):
    alst = [11, 8]
    for n in range(3, terms+1):
        alst.append(alst[-1] + alst[-2])
    return alst[:terms]
print(aupton(36)) # Michael S. Branicky, Nov 08 2021

Formula

From Andrew Howroyd, Aug 28 2018: (Start)

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

a(n) = 11*Fibonacci(n) - 3*Fibonacci(n-1).

G.f.: x*(11 - 3*x)/(1 - x - x^2). (End)