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

1,1

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).

Formula

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

Prog

(GAP) List([1..50], n->1944*n^2-5016*n+3138); # Muniru A Asiru, May 22 2018
(PARI) Vec(6*x*(11 + 114*x + 523*x^2)/(1 - x)^3 + O(x^40)) \\ Colin Barker, May 23 2018

Crossrefs

Cf. A082040, A304836, A304837.

Sequence in context: A229328 A101093 A293613 * A337896 A056468 A027785

Adjacent sequences: A304835 A304836 A304837 * A304839 A304840 A304841

Keyword

nonn,easy

Author

Emeric Deutsch, May 21 2018

Status

approved