A246176 The hyper-Wiener index of the Lucas cube Lambda(n) (n>=2).

5, 12, 66, 215, 789, 2597, 8540, 27153, 85135, 262482, 799566, 2408718, 7189343, 21282450, 62550312, 182664881, 530391339, 1532152571, 4405406030, 12613400079, 35974991437, 102242458164, 289632199980, 818005152300, 2303856458345, 6471890313480, 18136792078398

Offset: 2

Author

Emeric Deutsch, Aug 18 2014

Keywords

• nonn

Comments

The Lucas cube Lambda(n) can be defined as the graph whose vertices are the binary strings of length n without either two consecutive 1's or a 1 in the first and in the last position, and in which two vertices are adjacent when their Hamming distance is exactly 1.

Links

• G. G. Cash, Relationship between the Hosoya polynomial and the hyper-Wiener index, Appl. Math. Letters, 15, 2002, 893-895.
• S. Klavzar, M. Mollard, Wiener index and Hosoya polynomial of Fibonacci and Lucas cubes, MATCH Commun. Math. Comput. Chem., 68, 2012, 311-324.
• E. Munarini, C. P. Cippo, N. Z. Salvi, On the Lucas cubes, The Fibonacci Quarterly, 39, No. 1, 2001, 12-21.

Crossrefs

Cf. A246175.

Programs

Maple

g := z^2*(5-18*z+24*z^2-14*z^3+3*z^4-z^5)/((1+z)^3*(z^2-3*z+1)^3): gser := series(g, z = 0, 40): seq(coeff(gser, z, j), j = 2 .. 35);

Formula

G.f.: z^2(5-18z+24z^2-14z^3+3z^4-z^5)/((1+z)^3*(1-3*z+z^2)^3).