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
References
- Aamen Muharram, Investigations of the Gibonacci sequences: Simple Formulae and Gibonacci mod m.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1).
Programs
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Mathematica
LinearRecurrence[{1, 1}, {11, 26}, 35] (* Amiram Eldar, Aug 05 2022 *) -
Python
from gmpy2 import fib2 def A354383(n): return int(26*(a:=fib2(n))[0]+11*a[1]) # Chai Wah Wu, Aug 07 2022
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
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