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A304837
a(n) = 6*(n - 1)*(81*n - 104) for n >= 1.
3
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 21 2018
STATUS
approved