OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Fibonacci Cube Graph
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1).
FORMULA
a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).
G.f.: (x (-4 + 6 x + 3 x^2 - 4 x^3 - 2 x^4))/((-1 + x) (-1 + x + x^2)^2).
a(n) = (n*Lucas(n + 1) + Lucas(n + 4) - Fibonacci(n - 3))/5 + 1. - Ehren Metcalfe, Oct 16 2017
MATHEMATICA
LinearRecurrence[{3, -1, -3, 1, 1}, {4, 6, 11, 19, 34}, 20]
Table[((25 - 19 Sqrt[5]) (1 - Sqrt[5])^n + (1 + Sqrt[5])^n (25 + 19 Sqrt[5]))/(25 2^(n + 1)) + n LucasL[n + 1]/5 + 1, {n, 20}] // Expand
CoefficientList[Series[(-4 + 6 x + 3 x^2 - 4 x^3 - 2 x^4)/((-1 + x) (-1 + x + x^2)^2), {x, 0, 20}], x]
Table[(n LucasL[n + 1] + LucasL[n + 4] - Fibonacci[n - 3])/5 + 1, {n, 40}] (* Eric W. Weisstein, Nov 29 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 05 2017
STATUS
approved