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 A304511 a(n) = 318*2^n - 186 (n>=1). 4
 450, 1086, 2358, 4902, 9990, 20166, 40518, 81222, 162630, 325446, 651078, 1302342, 2604870, 5209926, 10420038, 20840262, 41680710, 83361606, 166723398, 333446982, 666894150, 1333788486, 2667577158, 5335154502, 10670309190, 21340618566, 42681237318, 85362474822, 170724949830, 341449899846, 682899799878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = the first Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf reference. 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 the dendrimer nanostar NS2[n] is M(NS2[n]; x,y) = 3*2^n*x*y^2 + (27*2^n - 24)*x^2*y^2 + (33*2^n - 18)*x^2*y^3 + 6*2^n*x^3*y^3. REFERENCES A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, No. 5-6, 2011, 1075-1080. 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. Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA From Colin Barker, May 15 2018: (Start) G.f.: 6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)). a(n) = 3*a(n-1) - 2*a(n-2) for n>2. (End) MAPLE seq(318*2^n-186, n = 1 .. 40); MATHEMATICA Array[318*2^# - 186 &, 31] (* Michael De Vlieger, May 14 2018 *) PROG (GAP) List([1..40], n->318*2^n-186); # Muniru A Asiru, May 15 2018 (PARI) Vec(6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018 CROSSREFS Cf. A304509, A304510, A304512. Sequence in context: A012062 A339978 A079659 * A202197 A253750 A253743 Adjacent sequences:  A304508 A304509 A304510 * A304512 A304513 A304514 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 14 2018 STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)