A277989 a(n) = 424*2^n + 37.

461, 885, 1733, 3429, 6821, 13605, 27173, 54309, 108581, 217125, 434213, 868389, 1736741, 3473445, 6946853, 13893669, 27787301, 55574565, 111149093, 222298149, 444596261, 889192485, 1778384933, 3556769829, 7113539621, 14227079205, 28454158373, 56908316709

Offset

0,1

Comments

a(n) is the second Zagreb index of the micelle-like chiral dendrimer B[n]. 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 pictorial definition of B[n] can be viewed in the Yousefi-Azari et al. references.

The M-polynomial of the micelle-like chiral dendrimer B[n] is M(B[n],x,y) = (8*2^n + 2)*x*y^2 + 12*x^2*y^2 + (56*2^n - 10)*x^2*y^3 + (8*2^n +5)*x^3*y^3.

Links

Table of n, a(n) for n=0..27.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

H. Yousefi-Azari, A. R. Ashrafi, and M. H. Khalifeh, Wiener index of micelle-like chiral dendrimers, Studia UBB, Chemia, 55, No. 4, 125-130, 2010.

H. Yousefi-Azari and A. R. Ashrafi, Computing PI index of micelle-like chiral dendrimers, Bulgarian Chem. Commun., 44, 4, 2012, 307-309.

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

Formula

G.f.: (461 - 498*x)/((1-x)*(1-2*x)).

Maple

seq(424*2^n+37, n = 0..35);

Mathematica

424*2^Range[0, 30]+37 (* or *) LinearRecurrence[{3, -2}, {461, 885}, 30] (* Harvey P. Dale, Feb 19 2018 *)

Prog

(Magma) [424*2^n+37: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016

Crossrefs

Cf. A277988.

Sequence in context: A107973 A227994 A142832 * A138956 A107121 A101734

Adjacent sequences: A277986 A277987 A277988 * A277990 A277991 A277992

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 12 2016

Status

approved