A304376 a(n) = 60*2^n - 48 (n>=1).

72, 192, 432, 912, 1872, 3792, 7632, 15312, 30672, 61392, 122832, 245712, 491472, 982992, 1966032, 3932112, 7864272, 15728592, 31457232, 62914512, 125829072, 251658192, 503316432, 1006632912, 2013265872, 4026531792, 8053063632, 16106127312, 32212254672, 64424509392, 128849018832

Offset

1,1

Comments

a(n) is the first Zagreb index of the triangulane T[n], defined pictorially in the Khalifeh et al. reference.

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

The M-polynomial of the triangulane T[n] is M(T[n]; x,y) = 3*2^{n-1}*x^2*y^2 + 3*2^n*x^2*y^4 + (9*2^{n-1}-6)*x^4*y^4.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, Computing Wiener and Kirchhoff indices of a triangulane, Indian J. Chemistry, 47A, 2008, 1503-1507.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Colin Barker, May 13 2018: (Start)

G.f.: 24*x*(3 - x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

(End)

Maple

seq(60*2^n - 48, n=1..40);

Prog

(PARI) Vec(24*x*(3 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 13 2018

Crossrefs

Cf. A304377.

Sequence in context: A044404 A044785 A254437 * A028977 A033693 A250786

Adjacent sequences: A304373 A304374 A304375 * A304377 A304378 A304379

Keyword

nonn,easy

Author

Emeric Deutsch, May 12 2018

Status

approved