A304512 a(n) = 366*2^n - 204 (n >= 1).

528, 1260, 2724, 5652, 11508, 23220, 46644, 93492, 187188, 374580, 749364, 1498932, 2998068, 5996340, 11992884, 23985972, 47972148, 95944500, 191889204, 383778612, 767557428, 1535115060, 3070230324, 6140460852, 12280921908, 24561844020, 49123688244, 98247376692, 196494753588

Offset

1,1

Comments

a(n) = the second Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf 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 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.: 12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(366*2^n-204, n = 1 .. 40);

Mathematica

Array[366*2^# - 204 &, 29] (* Michael De Vlieger, May 14 2018 *)

Prog

(GAP) List([1..40], n->366*2^n-204); # Muniru A Asiru, May 15 2018
(PARI) Vec(12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304509, A304510, A304511.

Sequence in context: A157475 A158365 A076580 * A037944 A282096 A223253

Adjacent sequences: A304509 A304510 A304511 * A304513 A304514 A304515

Keyword

nonn,easy

Author

Emeric Deutsch, May 14 2018

Status

approved