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 A305072 a(n) = 144*n^2 - 24*n (n>=1). 2
 120, 528, 1224, 2208, 3480, 5040, 6888, 9024, 11448, 14160, 17160, 20448, 24024, 27888, 32040, 36480, 41208, 46224, 51528, 57120, 63000, 69168, 75624, 82368, 89400, 96720, 104328, 112224, 120408, 128880, 137640, 146688, 156024, 165648, 175560, 185760, 196248, 207024, 218088, 229440, 241080, 253008, 265224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the first Zagreb index of the oxide network OX(n), defined pictorially in the Javaid et al. reference (Fig. 3, where OX(2) is shown) or in the Liu et al. reference (Fig. 6, where OX(5) is shown). 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 OX(n) is M(OX(n); x, y) = 12*n*x^2*y^4 + 6*n*(3*n - 2)*x^4*y^4 (n>=1). a(n) + 1 is a square. - Muniru A Asiru, May 27 2018 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..5000 E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102. M. Javaid and C. Y. Jung, M-polynomials and topological indices of silicate and oxide networks, International J. Pure and Applied Math., 115, No. 1, 2017, 129-152. J.-B. Liu, S. Wang, C. Wang, and S. Hayat, Further results on computation of topological indices of certain networks, IET Control Theory Appl., 11, No. 13, 2017, 2065-2071. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Colin Barker, May 26 2018: (Start) G.f.: 24*x*(5 + 7*x) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End) MAPLE seq(144*n^2 - 24*n, n = 1 .. 50); PROG (PARI) Vec(24*x*(5 + 7*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, May 26 2018 (GAP) List([1..50], n->144*n^2-24*n); # Muniru A Asiru, May 27 2018 CROSSREFS Cf. A305073. Sequence in context: A033697 A157960 A067915 * A221563 A336626 A241613 Adjacent sequences: A305069 A305070 A305071 * A305073 A305074 A305075 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 26 2018 STATUS approved

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Last modified November 29 19:18 EST 2023. Contains 367447 sequences. (Running on oeis4.)