

A304515


a(n) = 159*2^n  222 (n>=1).


4



96, 414, 1050, 2322, 4866, 9954, 20130, 40482, 81186, 162594, 325410, 651042, 1302306, 2604834, 5209890, 10420002, 20840226, 41680674, 83361570, 166723362, 333446946, 666894114, 1333788450, 2667577122, 5335154466, 10670309154, 21340618530, 42681237282, 85362474786, 170724949794, 341449899810, 682899799842, 1365799599906, 2731599200034, 5463198400290, 10926396800802, 21852793601826, 43705587203874
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OFFSET

1,1


COMMENTS

a(n) is the first Zagreb index of the nanostar dendrimer D[n] from the Ghorbani 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 D[n] is M(D[n]; x,y) = 12*(2^n  1)*x^2*y^2 + 3*(5*2^n  8)*x^2*y^3 + 3*(2*2^n  3)*x^3*y^3.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 5765.
Index entries for linear recurrences with constant coefficients, signature (3,2).


FORMULA

From Colin Barker, May 15 2018: (Start)
G.f.: 6*x*(16 + 21*x) / ((1  x)*(1  2*x)).
a(n) = 3*a(n1)  2*a(n2) for n>2.
(End)


MAPLE

seq(159*2^n222, n = 1 .. 40);


MATHEMATICA

Rest@ CoefficientList[Series[6 x (16 + 21 x)/((1  x) (1  2 x)), {x, 0, 38}], x] (* or *)
LinearRecurrence[{3, 2}, {96, 414}, 38] (* or *)
Array[159*2^#  222 &, 38] (* Michael De Vlieger, May 15 2018 *)


PROG

(GAP) List([1..40], n>159*2^n222); # Muniru A Asiru, May 15 2018
(PARI) Vec(6*x*(16 + 21*x) / ((1  x)*(1  2*x)) + O(x^40)) \\ Colin Barker, May 15 2018


CROSSREFS

Cf. A304513, A304514, A304516.
Sequence in context: A292543 A051465 A179825 * A233818 A233811 A233717
Adjacent sequences: A304512 A304513 A304514 * A304516 A304517 A304518


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 15 2018


STATUS

approved



