A305271 a(n) = 680*2^n - 548.

132, 812, 2172, 4892, 10332, 21212, 42972, 86492, 173532, 347612, 695772, 1392092, 2784732, 5570012, 11140572, 22281692, 44563932, 89128412, 178257372, 356515292, 713031132, 1426062812, 2852126172, 5704252892, 11408506332, 22817013212, 45634026972, 91268054492, 182536109532, 365072219612

Offset

0,1

Comments

a(n) is the first Zagreb index of the polyphenylene dendrimer G[n], defined pictorially in the Arif 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 the polyphenylene dendrimer G[n] is M(G[n]; x, y) = (56*2^n - 40)*x^2*y^2 + (48*2^n - 40)*x^2*y^3 +(36* 2^n - 36)*x^3*y^3 + 4*x^3 *y^4.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

N. E. Arif, Roslan Hasni and Saeid Alikhani, Fourth order and fourth sum connectivity indices of polyphenylene dendrimers, J. Applied Science, 12 (21), 2012, 2279-2282.

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 31 2018: (Start)

G.f.: 4*(33 + 104*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-548, n = 0..40);

Prog

(PARI) Vec(4*(33 + 104*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

Crossrefs

Cf. A305269, A305270, A305272.

Sequence in context: A115132 A158543 A156958 * A090199 A239598 A033278

Adjacent sequences: A305268 A305269 A305270 * A305272 A305273 A305274

Keyword

nonn,easy

Author

Emeric Deutsch, May 30 2018

Status

approved