A304377 a(n) = 102*2^n - 96 (n>=1).

108, 312, 720, 1536, 3168, 6432, 12960, 26016, 52128, 104352, 208800, 417696, 835488, 1671072, 3342240, 6684576, 13369248, 26738592, 53477280, 106954656, 213909408, 427818912, 855637920, 1711275936, 3422551968, 6845104032, 13690208160, 27380416416, 54760832928, 109521665952, 219043332000, 438086664096

Offset

1,1

Comments

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

The second Zagreb index of a simple connected graph is the sum of the degree products 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.

Wikipedia, Triangulane

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

Formula

From Colin Barker, May 13 2018: (Start)

G.f.: 12*x*(9 - x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(102*2^n - 96, n=1..40);

Prog

(PARI) Vec(12*x*(9 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 13 2018

Crossrefs

Cf. A304376.

Sequence in context: A204284 A204277 A138669 * A202616 A202609 A202100

Adjacent sequences: A304374 A304375 A304376 * A304378 A304379 A304380

Keyword

nonn,easy

Author

Emeric Deutsch, May 12 2018

Status

approved