A304837 a(n) = 6*(n - 1)*(81*n - 104) for n >= 1.

0, 348, 1668, 3960, 7224, 11460, 16668, 22848, 30000, 38124, 47220, 57288, 68328, 80340, 93324, 107280, 122208, 138108, 154980, 172824, 191640, 211428, 232188, 253920, 276624, 300300, 324948, 350568, 377160, 404724, 433260, 462768, 493248, 524700, 557124, 590520, 624888, 660228, 696540, 733824, 772080, 811308

Offset

1,2

Comments

a(n) is the first Zagreb index of the hex derived network HDN1(n) from the Manuel et al. reference (see HDN1(4) in Fig. 8).

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 HDN1(n) is M(HDN1(n); x, y) = 12*x^3*y^5 + (18*(n-2))*x^3*y^7 + (6*(3*n^2-9*n+7))*x^3*y^12 + 12*x^5*y^7 + 6*x^5*y^12 + (6*(n-3))*x^7*y^7 + (12*(n-2))*x^7*y^12 + (3*(n-2)*(3*n-5)*x^12*y^12.

54*a(n) + 529 is a square. - Bruno Berselli, May 22 2018

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.

P. Manuel, R. Bharati, I. Rajasingh, and Chris Monica M, On minimum metric dimension of honeycomb networks, J. Discrete Algorithms, 6, 2008, 20-27.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: 12*x^2*(29 + 52*x)/(1 - x)^3. - Bruno Berselli, May 22 2018

Maple

seq(624-1110*n+486*n^2, n = 1 .. 45);

Mathematica

Table[6 (n - 1) (81 n - 104), {n, 1, 50}] (* Bruno Berselli, May 22 2018 *)

Prog

(GAP) List([1..50], n->486*n^2-1110*n+624); # Muniru A Asiru, May 22 2018
(PARI) concat(0, Vec(12*x^2*(29 + 52*x)/(1 - x)^3 + O(x^40))) \\ Colin Barker, May 23 2018

Crossrefs

Cf. A082040, A304836, A304838.

Sequence in context: A293512 A275237 A129642 * A231089 A237318 A237724

Adjacent sequences: A304834 A304835 A304836 * A304838 A304839 A304840

Keyword

nonn,easy

Author

Emeric Deutsch, May 21 2018

Status

approved