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 A305068 a(n) = 54*n - 18 (n>=1). 2
 36, 90, 144, 198, 252, 306, 360, 414, 468, 522, 576, 630, 684, 738, 792, 846, 900, 954, 1008, 1062, 1116, 1170, 1224, 1278, 1332, 1386, 1440, 1494, 1548, 1602, 1656, 1710, 1764, 1818, 1872, 1926, 1980, 2034, 2088, 2142, 2196, 2250, 2304, 2358, 2412, 2466, 2520, 2574, 2628, 2682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the first Zagreb index of the chain silicate network CS(n), defined pictorially in the Javaid et al. reference (Fig. 2, where CS(6) is shown) or in Liu et al. reference (Fig. 4, where CS(8) 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 CS(n) is M(C(n);x,y) = (n+4)*x^3*y^3 + (4*n - 2)*x^3*y^6 + (n - 2)*x^6*y^6  (n>=2). 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 (2,-1). FORMULA From Colin Barker, May 26 2018: (Start) G.f.: 18*x*(2 + x) / (1 - x)^2. a(n) = 2*a(n-1) - a(n-2) for n>2. (End) MAPLE seq(54*n-18, n = 1..50); PROG (PARI) Vec(18*x*(2 + x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 26 2018 (GAP) List([1..50], n->54*n-18); # Muniru A Asiru, May 27 2018 CROSSREFS Cf. A305069. Sequence in context: A044174 A044555 A283635 * A182467 A060936 A247246 Adjacent sequences:  A305065 A305066 A305067 * A305069 A305070 A305071 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 25 2018 STATUS approved

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Last modified November 24 03:39 EST 2020. Contains 338607 sequences. (Running on oeis4.)