A304608 a(n) = 288*2^n + 178 (n >= 1).

754, 1330, 2482, 4786, 9394, 18610, 37042, 73906, 147634, 295090, 590002, 1179826, 2359474, 4718770, 9437362, 18874546, 37748914, 75497650, 150995122, 301990066, 603979954, 1207959730, 2415919282, 4831838386, 9663676594, 19327353010, 38654705842, 77309411506, 154618822834, 309237645490, 618475290802

Offset

1,1

Comments

a(n) is the second Zagreb index of the nanostar dendrimer G[n] from the Ashrafi 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 G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4.

Links

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

A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, Computing Wiener and detour indices of a new type of nanostar dendrimers, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.

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 Michael De Vlieger, May 16 2018: (Start)

G.f.: 2*x*(377 - 466*x)/(1 - 3*x + 2*x^2).

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

Maple

seq(288*2^n+178, n = 1 .. 40);

Mathematica

CoefficientList[Series[2 (377 - 466 x)/(1 - 3 x + 2 x^2), {x, 0, 30}], x] (* or *)
LinearRecurrence[{3, -2}, {754, 1330}, 31] (* or *)
Array[288*2^# + 178 &, 31] (* Michael De Vlieger, May 16 2018 *)

Prog

(PARI) a(n) = 288*2^n + 178; \\ Altug Alkan, May 15 2018
(PARI) Vec(2*x*(377 - 466*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 2018
(GAP) List([1..40], n->288*2^n+178); # Muniru A Asiru, May 16 2018

Crossrefs

Cf. A304605, A304606, A304607.

Sequence in context: A092449 A197107 A274235 * A252913 A252917 A252918

Adjacent sequences: A304605 A304606 A304607 * A304609 A304610 A304611

Keyword

nonn,easy

Author

Emeric Deutsch, May 15 2018

Status

approved