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A277988 a(n) = 352*2^n + 34. 1
386, 738, 1442, 2850, 5666, 11298, 22562, 45090, 90146, 180258, 360482, 720930, 1441826, 2883618, 5767202, 11534370, 23068706, 46137378, 92274722, 184549410, 369098786, 738197538, 1476395042, 2952790050, 5905580066, 11811160098, 23622320162, 47244640290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the first Zagreb index of the micelle-like chiral dendrimer B[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums 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.

I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.

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.: 2*(193 - 210*x)/((1-x)*(1-2*x)).

MAPLE

seq(352*2^n+34, n = 0..35);

MATHEMATICA

352*2^Range[0, 30]+34 (* or *) LinearRecurrence[{3, -2}, {386, 738}, 30] (* Harvey P. Dale, Jul 12 2021 *)

PROG

(Magma) [352*2^n+34: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016

CROSSREFS

Cf. A277989.

Sequence in context: A060721 A116316 A213115 * A224496 A230274 A230475

Adjacent sequences:  A277985 A277986 A277987 * A277989 A277990 A277991

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 12 2016

STATUS

approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)