A228702 Wiener index of generalized Fibonacci cube graph Q_n(111).

0, 1, 8, 36, 164, 694, 2792, 11008, 42484, 161395, 606000, 2252856, 8307224, 30424076, 110774704, 401307232, 1447463192, 5200692085, 18622103160, 66476800796, 236657676956, 840418968098, 2977799304536, 10529449821312, 37162248493740, 130933420076839

Offset

0,3

Links

Table of n, a(n) for n=0..25.

S. Klavzar and Y. Rho, On the Wiener index of generalized Fibonacci cubes and Lucas cubes, preprint (2013).

Formula

There is an explicit formula for a(n) in terms of tribonacci numbers (A000073).

Empirical g.f.: x*(x^2+1)*(x^2+4*x+1) / ((x^3-x^2-x-1)^2*(x^3+x^2+3*x-1)^2). - Colin Barker, Sep 08 2013

Prog

(Magma) /* From Klavzar and Rho paper, Theorem 2.4: */ T:=[n le 3 select Floor(n/3) else Self(n-1)+Self(n-2)+Self(n-3): n in [1..40]]; /* being T=A000073 */ [((268+67*n)*T[n+4]^2-(118+4*n)*T[n+4]*T[n+5]-(50-14*n)*T[n+4]*T[n+6] -(66+7*n)*T[n+5]^2+(90+16*n)*T[n+5]*T[n+6]-(18+6*n)*T[n+6]^2)/484: n in [0..#T-6]]; // Bruno Berselli, Sep 06 2013

Crossrefs

Cf. A000073.

Sequence in context: A055918 A074404 A221701 * A200667 A200468 A200250

Adjacent sequences: A228699 A228700 A228701 * A228703 A228704 A228705

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2013

Extensions

More terms from Bruno Berselli, Sep 06 2013

Status

approved