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A305156 a(n) = 136*2^n - 78 (n>=0). 3
58, 194, 466, 1010, 2098, 4274, 8626, 17330, 34738, 69554, 139186, 278450, 556978, 1114034, 2228146, 4456370, 8912818, 17825714, 35651506, 71303090, 142606258, 285212594, 570425266, 1140850610, 2281701298, 4563402674, 9126805426, 18253610930, 36507221938, 73014443954, 146028887986, 292057776050 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) (n>=0) is the first Zagreb index of the nanostar dendrimer G(n), defined pictorially in the Darafsheh et al. reference (see Fig. 1, where G(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 G(n) is M(G(n); x, y) = 8*2^n*x^2*y^2 + (16*2^n - 12)*x^2*y^3 + (4*2^n - 3)*x^3*y^3
REFERENCES
M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
FORMULA
From Colin Barker, May 29 2018: (Start)
G.f.: 2*(29 + 10*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(136*2^n-78, n = 0 .. 40);
PROG
(PARI) Vec(2*(29 + 10*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
Sequence in context: A067914 A250800 A172357 * A334186 A051972 A027987
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 28 2018
STATUS
approved

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Last modified April 20 04:17 EDT 2024. Contains 371798 sequences. (Running on oeis4.)