

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
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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 Mpolynomial 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, 193200.
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
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



