The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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