A277105 a(n) = (27*3^n - 63)/2.

9, 90, 333, 1062, 3249, 9810, 29493, 88542, 265689, 797130, 2391453, 7174422, 21523329, 64570050, 193710213, 581130702, 1743392169, 5230176570, 15690529773, 47071589382, 141214768209, 423644304690, 1270932914133, 3812798742462, 11438396227449, 34315188682410, 102945566047293, 308836698141942, 926510094425889

Offset: 1

Author

Emeric Deutsch, Nov 05 2016

Keywords

• nonn
• easy

Comments

a(n) is the second Zagreb index of the Hanoi graph H[n] (n>=2).

The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.

The M-polynomial of the Hanoi graph H[n] is M(H[n],x,y) = 6*x^2*y^3 + (3/2)*(3^n - 5)*x^3*y^3.

Links

• E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
• Eric Weisstein's World of Mathematics, Hanoi Graph
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A116970, A277104.

Programs

Magma

[(27*3^n-63)/2: n in [1..30]]; // Bruno Berselli, Nov 14 2016

Maple

seq((1/2)*(9*(3^(n+1)-7)), n = 1..30);

Mathematica

Table[(27 3^n - 63)/2, {n, 1, 30}] (* Bruno Berselli, Nov 14 2016 *)

Formula

O.g.f.: 9*x*(1 + 6*x)/((1 - x)*(1 - 3*x)).

E.g.f.: 9*(1 - exp(x))*(4 - 3*exp(x) - 3*exp(2*x))/2. - Bruno Berselli, Nov 14 2016

a(n) = 9*A116970(n+1).