A304516 a(n) = 192*2^n - 273 (n>=1).

111, 495, 1263, 2799, 5871, 12015, 24303, 48879, 98031, 196335, 392943, 786159, 1572591, 3145455, 6291183, 12582639, 25165551, 50331375, 100663023, 201326319, 402652911, 805306095, 1610612463, 3221225199, 6442450671, 12884901615, 25769803503, 51539607279, 103079214831, 206158429935, 412316860143, 824633720559

Offset

1,1

Comments

a(n) is the second Zagreb index of the nanostar dendrimer D[n] from the Ghorbani et al. 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 D[n] is M(D[n]; x,y) = 12*(2^n - 1)*x^2*y^2 + 3*(5*2^n - 8)*x^2*y^3 + 3*(2*2^n - 3)*x^3*y^3.

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.

M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.

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

Formula

From Colin Barker, May 15 2018: (Start)

G.f.: 3*x*(37 + 54*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(192*2^n-273, n = 1 .. 40);

Mathematica

Rest@ CoefficientList[Series[3 x (37 + 54 x)/((1 - x) (1 - 2 x)), {x, 0, 32}], x] (* or *)
LinearRecurrence[{3, -2}, {111, 495}, 32] (* or *)
Array[192*2^# - 273 &, 32] (* Michael De Vlieger, May 15 2018 *)

Prog

(GAP) List([1..40], n->192*2^n-273); # Muniru A Asiru, May 15 2018
(PARI) Vec(3*x*(37 + 54*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304513, A304514, A304515.

Sequence in context: A277960 A304831 A364023 * A259246 A205830 A302228

Adjacent sequences: A304513 A304514 A304515 * A304517 A304518 A304519

Keyword

nonn,easy

Author

Emeric Deutsch, May 15 2018

Status

approved