A304615 a(n) = 507*2^n - 273.

234, 741, 1755, 3783, 7839, 15951, 32175, 64623, 129519, 259311, 518895, 1038063, 2076399, 4153071, 8306415, 16613103, 33226479, 66453231, 132906735, 265813743, 531627759, 1063255791, 2126511855, 4253023983, 8506048239, 17012096751, 34024193775, 68048387823, 136096775919, 272193552111

Offset

0,1

Comments

a(n) is the second Zagreb index of the nanostar dendrimer NS[n] from the Mirzargar reference.

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 NS[n] is M(NS[n]; x,y) = (30*2^n - 12)*x^2*y^2 + (42*2^n - 24)*x^2*y^3 + (15*2^n - 9)*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. Mirzargar, PI, Szeged and edge Szeged polynomials of a dendrimer nanostar, MATCH, Commun. Math. Comput. Chem. 62, 2009, 363-370.

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

Formula

From Colin Barker, May 18 2018: (Start)

G.f.: 39*(6 + x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(507*2^n - 273, n = 0 .. 40);

Mathematica

Table[507*2^n-273, {n, 0, 30}] (* Harvey P. Dale, Jul 17 2019 *)

Prog

(PARI) Vec(39*(6 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018

Crossrefs

Cf. A304612, A304613, A304614.

Sequence in context: A186897 A184450 A338391 * A287878 A252338 A252777

Adjacent sequences: A304612 A304613 A304614 * A304616 A304617 A304618

Keyword

nonn,easy

Author

Emeric Deutsch, May 16 2018

Status

approved