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 A305070 a(n) = 378*n^2 - 54*n (n>=1). 2
 324, 1404, 3240, 5832, 9180, 13284, 18144, 23760, 30132, 37260, 45144, 53784, 63180, 73332, 84240, 95904, 108324, 121500, 135432, 150120, 165564, 181764, 198720, 216432, 234900, 254124, 274104, 294840, 316332, 338580, 361584, 385344, 409860, 435132, 461160, 487944, 515484, 543780, 572832, 602640, 633204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the first Zagreb index of the silicate network SL(n), defined pictorially in the Javaid et al. reference (Fig. 1, where SL(2) is shown) or in Liu et al. reference (Fig. 3, where again SL(2) 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 SL(n) is M(SL(n);x,y) = 6*n*x^3*y^3 + (18*n^2 + 6*n)*x^3*y^6 + (18*n^2 - 12*n)*x^6*y^6 (n>=2). 14*a(n)/27 + 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.: 108*x*(3 + 4*x) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End) MAPLE seq(378*n^2 - 54*n, n = 1 .. 50); MATHEMATICA Table[378n^2-54n, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 324, 1404}, 50] (* Harvey P. Dale, Jan 29 2023 *) PROG (PARI) Vec(108*x*(3 + 4*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, May 26 2018 (GAP) List([1..50], n->378*n^2-54*n); # Muniru A Asiru, May 27 2018 CROSSREFS Cf. A305071. Sequence in context: A329613 A202094 A202486 * A229538 A250437 A064197 Adjacent sequences: A305067 A305068 A305069 * A305071 A305072 A305073 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 25 2018 STATUS approved

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Last modified September 16 17:53 EDT 2024. Contains 375976 sequences. (Running on oeis4.)