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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

Colin Barker, Table of n, a(n) for n = 0..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 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

Cf. A226264, A305155, A305157.

Sequence in context: A067914 A250800 A172357 * A334186 A051972 A027987

Adjacent sequences:  A305153 A305154 A305155 * A305157 A305158 A305159

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 28 2018

STATUS

approved

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Last modified May 17 00:16 EDT 2021. Contains 343957 sequences. (Running on oeis4.)