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 A304504 a(n) = 3*(3*n+1)*(9*n+8)/2. 2
 12, 102, 273, 525, 858, 1272, 1767, 2343, 3000, 3738, 4557, 5457, 6438, 7500, 8643, 9867, 11172, 12558, 14025, 15573, 17202, 18912, 20703, 22575, 24528, 26562, 28677, 30873, 33150, 35508, 37947, 40467, 43068, 45750, 48513, 51357, 54282, 57288, 60375, 63543, 66792 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The second Zagreb index of the single-defect 3-gonal nanocone CNC(3,n) (see definition in the Doslic et al. reference, p. 27). 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 CNC(3,n) is M(CNC(3,n); x,y) = 3*x^2*y^2 + 6*n*x^2*y^3 + 3*n*(3*n+1)*x^3*y^3/2. More generally, the M-polynomial of CNC(k,n) is M(CNC(k,n); x,y) = k*x^2*y^2 + 2*k*n*x^2*y^3 + k*n*(3*n + 1)*x^3*y^3/2. 8*a(n) + 25 is a square. - Bruno Berselli, May 14 2018 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102. T. Doslic and M. Saheli, Augmented eccentric connectivity index of single-defect nanocones, J. of Mathematical Nanoscience, 1, No. 1, 2011, 25-31. A. Khaksar, M. Ghorbani, and H. R. Maimani, On atom bond connectivity and GA indices of nanocones, Optoelectronics and Advanced Materials - Rapid Communications, 4, No. 11, 2010, 1868-1870. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Colin Barker, May 14 2018: (Start) G.f.: 3*(4 + 22*x + x^2) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End) MAPLE seq((1/2)*(3*(9*n+8))*(3*n+1), n = 0 .. 40); PROG (PARI) Vec(3*(4 + 22*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 14 2018 CROSSREFS Cf. A304503. Sequence in context: A109020 A099299 A344366 * A344279 A022736 A261483 Adjacent sequences:  A304501 A304502 A304503 * A304505 A304506 A304507 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 13 2018 STATUS approved

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)