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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

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)

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000045.

Sequence in context: A306494 A068974 A244447 * A304699 A377042 A133236

Adjacent sequences: A206417 A206418 A206419 * A206421 A206422 A206423

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Status

approved