

A304389


a(n) = 126*2^n  22 (n>=1).


2



230, 482, 986, 1994, 4010, 8042, 16106, 32234, 64490, 129002, 258026, 516074, 1032170, 2064362, 4128746, 8257514, 16515050, 33030122, 66060266, 132120554, 264241130, 528482282, 1056964586, 2113929194, 4227858410, 8455716842, 16911433706, 33822867434, 67645734890, 135291469802, 270582939626, 541165879274
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OFFSET

1,1


COMMENTS

a(n) is the first Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
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 NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n + 3)x^2*y^2 + (18*2^n  12)x^2*y^3 + 3x^3*y^4 .


LINKS



FORMULA

G.f.: 2*x*(115  104*x) / ((1  x)*(1  2*x)).
a(n) = 3*a(n1)  2*a(n2) for n>2.
(End)


MAPLE

seq(126*2^n22, n = 1 .. 40);


PROG

(PARI) a(n) = 126*2^n  22; \\ Altug Alkan, May 13 2018
(PARI) Vec(2*x*(115  104*x) / ((1  x)*(1  2*x)) + O(x^40)) \\ Colin Barker, May 18 2018


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



