OFFSET
0,3
COMMENTS
See A346513 for Fibonacci(n+1)^3 - Fibonacci(n)^3.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1595
Feryal Alayont and Evan Henning, Edge Covers of Caterpillars, Cycles with Pendants, and Spider Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.9.4.
Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
FORMULA
a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4).
G.f.: x*(1 + 4*x - x^2)/(1 - 3*x - 6*x^2 + 3*x^3 + x^4).
a(n) = (4/5)*Fibonacci(3*n) + (-1)^(n)*(3/5)*Fibonacci(n).
a(n) is the numerator of the continued fraction [1,...,1, 2 ,1,...,1, 2 ,1,1,...,1] with the first two runs of 1's of length n-2 and the last run of length n-1. For example, a(4)=117 which is the numerator of the continued fraction [1,1, 2 ,1,1, 2 ,1,1,1].
MATHEMATICA
Differences[Fibonacci[Range[-1, 26]]^3, 1, 2]
PROG
(Python)
from sympy import fibonacci
def A350473(n): return fibonacci(n+1)**3-fibonacci(n-1)**3 # Chai Wah Wu, Jan 05 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresden, Jan 01 2022
STATUS
approved