

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
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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 Mpolynomial 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, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
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, 247252.
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(n1)  2*a(n2) for n>1.
(End)


MAPLE

seq(680*2^n622, 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



