A291916 Number of (not necessarily maximal) cliques in the n-Fibonacci cube graph.

4, 6, 11, 19, 34, 60, 106, 186, 325, 565, 978, 1686, 2896, 4958, 8463, 14407, 24466, 41456, 70102, 118322, 199369, 335401, 563426, 945194, 1583644, 2650230, 4430291, 7398331, 12342850, 20573220, 34262338, 57013866, 94800781, 157517533, 261545778, 433993662

Offset

1,1

Links

Table of n, a(n) for n=1..36.

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

Cf. A022137, A001629 (maximum and maximal cliques).

Sequence in context: A197985 A058579 A022318 * A047811 A244010 A154145

Adjacent sequences: A291913 A291914 A291915 * A291917 A291918 A291919

Keyword

nonn

Author

Eric W. Weisstein, Sep 05 2017

Status

approved