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 A304165 a(n) = 324*n^2 - 336*n + 102 (n >= 1). 2
 90, 726, 2010, 3942, 6522, 9750, 13626, 18150, 23322, 29142, 35610, 42726, 50490, 58902, 67962, 77670, 88026, 99030, 110682, 122982, 135930, 149526, 163770, 178662, 194202, 210390, 227226, 244710, 262842, 281622, 301050, 321126, 341850, 363222, 385242, 407910, 431226, 455190, 479802, 505062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the first Zagreb index of the HcDN1(n) network (see Fig. 3 in the Hayat et al. manuscript). 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 HcDN1(n) is M(HcDN1(n);x,y) = 6x^3*y^3 + 12(n-1)x^3*y^5 + 6nx^3*y^6 + 18(n-1)x^5*y^6 + (27n^2 -57n +30)x^6*y^6. - Emeric Deutsch, May 11 2018 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102. S. Hayat, M. A. Malik, and M. Imran, Computing topological indices of honeycomb derived networks, Romanian J. of Information Science and Technology, 18, No. 2, 2015, 144-165. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Colin Barker, May 10 2018: (Start) G.f.: 6*x*(15 + 76*x + 17*x^2) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End) MAPLE seq(324*n^2-336*n+102, n=1..40); MATHEMATICA Table[324n^2-336n+102, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {90, 726, 2010}, 40] (* Harvey P. Dale, Apr 12 2020 *) PROG (PARI) a(n) = 324*n^2-336*n+102; \\ Altug Alkan, May 09 2018 (PARI) Vec(6*x*(15 + 76*x + 17*x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, May 10 2018 (GAP) List([1..40], n->324*n^2-336*n+102); # Muniru A Asiru, May 10 2018 CROSSREFS Cf. A304163, A304164, A304166. Sequence in context: A065949 A224541 A051695 * A232588 A097372 A263170 Adjacent sequences:  A304162 A304163 A304164 * A304166 A304167 A304168 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 09 2018 STATUS approved

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Last modified August 9 12:05 EDT 2022. Contains 356026 sequences. (Running on oeis4.)