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A304607 a(n) = 252*2^n + 140 (n>=1). 4
644, 1148, 2156, 4172, 8204, 16268, 32396, 64652, 129164, 258188, 516236, 1032332, 2064524, 4128908, 8257676, 16515212, 33030284, 66060428, 132120716, 264241292, 528482444, 1056964748, 2113929356, 4227858572, 8455717004, 16911433868, 33822867596, 67645735052, 135291469964, 270582939788, 541165879436, 1082331758732 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the first Zagreb index of the nanostar dendrimer G[n] from the Ashrafi et al. reference.

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums 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 15 2018: (Start)

G.f.: 28*x*(23 - 28*x)/(1 - 3*x + 2*x^2).

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

MAPLE

seq(252*2^n+140, n = 1 .. 40);

MATHEMATICA

CoefficientList[Series[28*(23 - 28*x)/(1 - 3*x + 2*x^2), {x, 0, 31}], x] (* or *)

LinearRecurrence[{3, -2}, {644, 1148}, 32] (* or *)

Array[252*2^# + 140 &, 32] (* Michael De Vlieger, May 15 2018 *)

PROG

(PARI) a(n) = 252*2^n + 140; \\ Altug Alkan, May 15 2018

(PARI) Vec(28*x*(23 - 28*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 2018

(GAP) List([1..40], n->252*2^n+140); # Muniru A Asiru, May 16 2018

CROSSREFS

Cf. A304605, A304606, A304608.

Sequence in context: A089295 A195808 A260838 * A168626 A216023 A100873

Adjacent sequences:  A304604 A304605 A304606 * A304608 A304609 A304610

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 15 2018

STATUS

approved

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Last modified October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)