A220361 a(n) = Fibonacci(n)^3 + (-1)^n*Fibonacci(n-2).
1, 7, 28, 123, 515, 2192, 9269, 39291, 166396, 704935, 2986039, 12649248, 53582777, 226980767, 961505180, 4073002563, 17253513691, 73087060144, 309601749709, 1311494066355, 5555578003196, 23533806098447, 99690802365743, 422297015611968, 1788878864731825
Offset: 2
References
- R. K. Guy, Unsolved Problems in Number Theory, D20.
Links
- Indranil Ghosh, Table of n, a(n) for n = 2..1593
- J. H. Jordan and B. E. Peterson, Almost regular integer Fibonacci pentagons, Rocky Mountain J. Math. Volume 23, Number 1 (1993), 243-247.
- Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
Programs
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Maple
with(combinat): A220361:=n->fibonacci(n)^3+(-1)^n*fibonacci(n-2): seq(A220361(n), n=2..30); # Wesley Ivan Hurt, Apr 26 2017
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Mathematica
Table[Fibonacci[n]^3 + (-1)^n * Fibonacci[n - 2], {n, 2, 30}] (* T. D. Noe, Dec 13 2012 *) LinearRecurrence[{3,6,-3,-1},{1,7,28,123},30] (* Harvey P. Dale, Jul 13 2021 *) -
PARI
Vec(x^2*(x^2+4*x+1)/((x^2-x-1)*(x^2+4*x-1)) + O(x^100)) \\ Colin Barker, Sep 23 2014
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PARI
a(n) = fibonacci(n)^3 + (-1)^n*fibonacci(n-2) \\ Charles R Greathouse IV, Feb 14 2017
Formula
a(n) = 3*a(n-1)+6*a(n-2)-3*a(n-3)-a(n-4). G.f.: x^2*(x^2+4*x+1) / ((x^2-x-1)*(x^2+4*x-1)). - Colin Barker, Sep 23 2014
a(n) = F(n-1)*(F(n+1)*F(n) - (-1)^n). - Greg Dresden, Sep 04 2025
Comments