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 A350473 a(n) = Fibonacci(n+1)^3 - Fibonacci(n-1)^3. 1
 0, 1, 7, 26, 117, 485, 2072, 8749, 37107, 157114, 665665, 2819609, 11944368, 50596649, 214331663, 907922170, 3846022173, 16292007901, 69014058568, 292348234421, 1238407008795, 5245976249306, 22222312038857, 94135224351601, 398763209531232, 1689188062337425 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000045, A110224, A346513. Sequence in context: A026617 A240261 A232605 * A349309 A262110 A319425 Adjacent sequences: A350470 A350471 A350472 * A350474 A350475 A350476 KEYWORD nonn,easy AUTHOR Greg Dresden, Jan 01 2022 STATUS approved

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Last modified June 17 06:25 EDT 2024. Contains 373432 sequences. (Running on oeis4.)