A304511 a(n) = 318*2^n - 186 (n>=1).

450, 1086, 2358, 4902, 9990, 20166, 40518, 81222, 162630, 325446, 651078, 1302342, 2604870, 5209926, 10420038, 20840262, 41680710, 83361606, 166723398, 333446982, 666894150, 1333788486, 2667577158, 5335154502, 10670309190, 21340618566, 42681237318, 85362474822, 170724949830, 341449899846, 682899799878

Offset

1,1

Comments

a(n) = the first Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf reference.

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 dendrimer nanostar NS2[n] is M(NS2[n]; x,y) = 3*2^n*x*y^2 + (27*2^n - 24)*x^2*y^2 + (33*2^n - 18)*x^2*y^3 + 6*2^n*x^3*y^3.

References

A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, No. 5-6, 2011, 1075-1080.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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 15 2018: (Start)

G.f.: 6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(318*2^n-186, n = 1 .. 40);

Mathematica

Array[318*2^# - 186 &, 31] (* Michael De Vlieger, May 14 2018 *)
LinearRecurrence[{3, -2}, {450, 1086}, 40] (* Harvey P. Dale, Sep 09 2021 *)

Prog

(GAP) List([1..40], n->318*2^n-186); # Muniru A Asiru, May 15 2018
(PARI) Vec(6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304509, A304510, A304512.

Sequence in context: A339978 A351947 A079659 * A202197 A253750 A253743

Adjacent sequences: A304508 A304509 A304510 * A304512 A304513 A304514

Keyword

nonn,easy

Author

Emeric Deutsch, May 14 2018

Status

approved