A277104 a(n) = 9*3^n - 15.

12, 66, 228, 714, 2172, 6546, 19668, 59034, 177132, 531426, 1594308, 4782954, 14348892, 43046706, 129140148, 387420474, 1162261452, 3486784386, 10460353188, 31381059594, 94143178812, 282429536466, 847288609428, 2541865828314, 7625597484972, 22876792454946

Offset: 1

Author

Emeric Deutsch, Nov 05 2016

Keywords

• nonn
• easy

Comments

a(n) is the first Zagreb index of the Hanoi graph H[n].

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph.

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.
• I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
• Eric. W. Weisstein's World of Mathematics, Hanoi Graph
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A277105.

Programs

Magma

[9*3^n-15: n in [1..30]]; // Bruno Berselli, Nov 14 2016

Maple

seq(9*3^n-15, n = 1..30);

Mathematica

Table[9 3^n - 15, {n, 1, 30}] (* Bruno Berselli, Nov 14 2016 *)

PARI

a(n)=3^(n+2)-15 \\ Charles R Greathouse IV, Nov 14 2016

Formula

O.g.f.: 6*x*(2 + 3*x)/((1 - x)*(1 - 3*x)).

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

a(n) = 3*A168613(n+1). - R. J. Mathar, Apr 07 2022