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 A304519 a(n) = 72*2^n -56 (n>=1). 2
 88, 232, 520, 1096, 2248, 4552, 9160, 18376, 36808, 73672, 147400, 294856, 589768, 1179592, 2359240, 4718536, 9437128, 18874312, 37748680, 75497416, 150994888, 301989832, 603979720, 1207959496, 2415919048, 4831838152, 9663676360, 19327352776, 38654705608, 77309411272, 154618822600, 309237645256, 618475290568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the second Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference. The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph. The M-polynomial of NS2[n] is M(NS2[n]; x,y) = 2*2^n *x*y^2 + (8*2^n - 5)*x^2*y^2 + (6*2^n - 6)*x^2*y^3. 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. A. Madanshekaf and M. Moradi, The first geometric-arithmetic index of some nanostar dendrimers, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6. Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA From Colin Barker, May 15 2018: (Start) G.f.: 8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)). a(n) = 3*a(n-1) - 2*a(n-2) for n>2. (End) MAPLE seq(72*2^n-56, n = 1 .. 40); PROG (GAP) List([1..40], n->72*2^n-56); # Muniru A Asiru, May 15 2018 (PARI) Vec(8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018 CROSSREFS Cf. A304517, A304518. Sequence in context: A184022 A116448 A046330 * A261142 A328872 A001347 Adjacent sequences:  A304516 A304517 A304518 * A304520 A304521 A304522 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 15 2018 STATUS approved

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Last modified September 28 22:34 EDT 2021. Contains 347717 sequences. (Running on oeis4.)