A354383 Fibonacci sequence beginning 11, 26.

11, 26, 37, 63, 100, 163, 263, 426, 689, 1115, 1804, 2919, 4723, 7642, 12365, 20007, 32372, 52379, 84751, 137130, 221881, 359011, 580892, 939903, 1520795, 2460698, 3981493, 6442191, 10423684, 16865875, 27289559, 44155434, 71444993, 115600427, 187045420

Offset

0,1

Comments

The Pisano period of this sequence is equal to the Pisano period of the Fibonacci sequence for all non-multiples of 269.

References

Aamen Muharram, Investigations of the Gibonacci sequences: Simple Formulae and Gibonacci mod m.

Links

Table of n, a(n) for n=0..34.

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

Formula

a(n) = F(n-4) + L(n+1) + F(n+7).

a(n) = 2*F(n-1) + 3*F(n+4) + 11*F(n).

a(n) = 3*F(n+5) - 2*F(n-3).

a(n) = L(n-3) + L(n+6) - 3*F(n+2), where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number.

G.f.: (11+15*x)/(1-x-x^2).

a(n) = 11*F(n-1) + 26*F(n). - Chai Wah Wu, Aug 07 2022

Mathematica

LinearRecurrence[{1, 1}, {11, 26}, 35] (* Amiram Eldar, Aug 05 2022 *)

Prog

(C++) int a[int n]; int * aSequence(){a[0]=11; a[1]=26; for(int i=2; i<n; i++) a[i]=a[i-2]+a[i-1]; return a; }
(Python)
from gmpy2 import fib2
def A354383(n): return int(26*(a:=fib2(n))[0]+11*a[1]) # Chai Wah Wu, Aug 07 2022

Crossrefs

Cf. A000032, A000045.

Sequence in context: A247466 A329809 A190684 * A002154 A035934 A035932

Adjacent sequences: A354380 A354381 A354382 * A354384 A354385 A354386

Keyword

nonn,easy

Author

Aamen Muharram, Aug 04 2022

Status

approved