A277104 -id:A277104 - cp's OEIS frontend

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

Emeric Deutsch, Nov 05 2016

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.

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).

Cf. A116970, A277104.

[(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);
```

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

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).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula