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A305263 a(n) = 680*2^n - 622. 4
58, 738, 2098, 4818, 10258, 21138, 42898, 86418, 173458, 347538, 695698, 1392018, 2784658, 5569938, 11140498, 22281618, 44563858, 89128338, 178257298, 356515218, 713031058, 1426062738, 2852126098, 5704252818, 11408506258, 22817013138, 45634026898, 91268054418, 182536109458, 365072219538, 730144439698 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the first Zagreb index of the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).

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 nanostar dendrimer G[n] is M(G[n];x,y) = (56*2^n - 48)*x^2*y^2 + (48*2^n - 44)*x^2*y^3 +(36* 2^n - 35)*x^3*y^3.

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.

M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

From Colin Barker, May 31 2018: (Start)

G.f.: 2*(29 + 282*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

(End)

MAPLE

seq(680*2^n-622, n = 0..40);

PROG

(PARI) Vec(2*(29 + 282*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

CROSSREFS

Cf. A305261, A305262, A305264.

Sequence in context: A204470 A254954 A172215 * A157252 A142966 A093258

Adjacent sequences:  A305260 A305261 A305262 * A305264 A305265 A305266

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 29 2018

STATUS

approved

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)