A305268 a(n) = 82*2^n + 440.

522, 604, 768, 1096, 1752, 3064, 5688, 10936, 21432, 42424, 84408, 168376, 336312, 672184, 1343928, 2687416, 5374392, 10748344, 21496248, 42992056, 85983672, 171966904, 343933368, 687866296, 1375732152, 2751463864, 5502927288, 11005854136, 22011707832, 44023415224, 88046830008, 176093659576

Offset

0,1

Comments

a(n) is the second Zagreb index of the first type of dendrimer nanostar G[n], shown pictorially in the Iranmanesh et al. reference (Fig. 1).

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 the dendrimer nanostar G[n] is M(G[n]; x, y) = (4*2^n + 23)*x^2*y^2 + (8*2^n + 34)*x^2*y^3 + (2*2^n + 16)*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.

A. Iranmanesh, N. A. Gholami, Computing the Szeged index of two type dendrimer nanostars, Croatica Chemica Acta, 81, No. 2, 2008, 299-303.

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

Formula

From Colin Barker, May 30 2018: (Start)

G.f.: 2*(261 - 481*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(82*2^n+440, n = 0..40);

Prog

(PARI) Vec(2*(261 - 481*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A305265, A305266, A305267.

Sequence in context: A033525 A138647 A045050 * A004968 A263306 A128809

Adjacent sequences: A305265 A305266 A305267 * A305269 A305270 A305271

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved