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A354383 Fibonacci sequence beginning 11, 26. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A247466 A329809 A190684 * A002154 A035934 A035932
KEYWORD
nonn,easy
AUTHOR
Aamen Muharram, Aug 04 2022
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)