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A248086 Sum of the eccentricities of all vertices in the Lucas cube Lambda(n). 0
0, 0, 5, 7, 22, 37, 81, 143, 276, 490, 895, 1578, 2802, 4894, 8547, 14797, 25560, 43919, 75267, 128525, 218930, 371920, 630465, 1066452, 1800612, 3034812, 5106881, 8580883, 14398426, 24129145, 40388085, 67527563, 112786512 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The vertex set of the Lucas cube Lambda(n) is the set of all binary strings of length n without consecutive 1's and without a 1 in the first and the last bit. Two vertices of the Lucas cube are adjacent if their strings differ in exactly one bit.

a(n) = Sum(k*A210572(n,k), k=0..n).

LINKS

Table of n, a(n) for n=0..32.

A. Castro and M. Mollard, The eccentricity sequences of Fibonacci and Lucas cubes, Discrete Math., 312 (2012), 1025-1037.

S. Klavzar, M. Mollard, Asymptotic Properties of Fibonacci Cubes and Lucas Cubes, Annals of Combinatorics, 18, 2014, 447-457.

Index entries for linear recurrences with constant coefficients, signature (1,4,-2,-6,0,3,1).

FORMULA

a(n) = n*F(n+1) + (-1)^n*(n - floor(n/2)), where F(n) = A000045(n) are the Fibonacci numbers; see the formula for e'_n on p. 450 of the Klavzar - Mollard reference.

G.f.: z^2*(5 + 2*z - 5*z^2 - 3*z^3)/((1 + z)*(1 - z^2)*(1 - z - z^2)^2).

EXAMPLE

a(2) = 5; indeed Lambda(2) is the path on 3 vertices with eccentricities 2, 1, 2.

a(3) = 7; indeed Lambda(3) is the star on 4 vertices with eccentricities 1, 2, 2, 2.

MAPLE

with(combinat): a := n -> n*fibonacci(n+1) + (-1)^n*(n-floor(n/2)); seq(a(n), n = 0 .. 40);

CROSSREFS

Cf. A000045, A210572.

Sequence in context: A165144 A084164 A036498 * A076409 A294154 A260658

Adjacent sequences:  A248083 A248084 A248085 * A248087 A248088 A248089

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 01 2014

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)