A304838 a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).

66, 882, 5586, 14178, 26658, 43026, 63282, 87426, 115458, 147378, 183186, 222882, 266466, 313938, 365298, 420546, 479682, 542706, 609618, 680418, 755106, 833682, 916146, 1002498, 1092738, 1186866, 1284882, 1386786, 1492578, 1602258, 1715826, 1833282, 1954626, 2079858

Offset: 1

Author

Emeric Deutsch, May 21 2018

Keywords

• nonn
• easy

Comments

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

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 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.

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).

Crossrefs

Cf. A082040, A304836, A304837.

Programs

GAP

List([1..50], n->1944*n^2-5016*n+3138); # Muniru A Asiru, May 22 2018

Maple

seq(3138 - 5016*n + 1944*n^2, n = 1 .. 45);

Mathematica

Table[1944 n^2 - 5016 n + 3138, {n, 1, 40}] (* Bruno Berselli, May 22 2018 *)
LinearRecurrence[{3,-3,1},{66,882,5586},40] (* Harvey P. Dale, Dec 02 2018 *)

PARI

Vec(6*x*(11 + 114*x + 523*x^2)/(1 - x)^3 + O(x^40)) \\ Colin Barker, May 23 2018

Formula

G.f.: 6*x*(11 + 114*x + 523*x^2)/(1 - x)^3. - Bruno Berselli, May 22 2018