

A305068


a(n) = 54*n  18 (n>=1).


2



36, 90, 144, 198, 252, 306, 360, 414, 468, 522, 576, 630, 684, 738, 792, 846, 900, 954, 1008, 1062, 1116, 1170, 1224, 1278, 1332, 1386, 1440, 1494, 1548, 1602, 1656, 1710, 1764, 1818, 1872, 1926, 1980, 2034, 2088, 2142, 2196, 2250, 2304, 2358, 2412, 2466, 2520, 2574, 2628, 2682
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OFFSET

1,1


COMMENTS

a(n) is the first Zagreb index of the chain silicate network CS(n), defined pictorially in the Javaid et al. reference (Fig. 2, where CS(6) is shown) or in Liu et al. reference (Fig. 4, where CS(8) is shown).
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 CS(n) is M(C(n);x,y) = (n+4)*x^3*y^3 + (4*n  2)*x^3*y^6 + (n  2)*x^6*y^6 (n>=2).


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..5000
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
M. Javaid and C. Y. Jung, Mpolynomials and topological indices of silicate and oxide networks, International J. Pure and Applied Math., 115, No. 1, 2017, 129152.
J.B. Liu, S. Wang, C. Wang, and S. Hayat, Further results on computation of topological indices of certain networks, IET Control Theory Appl., 11, No. 13, 2017, 20652071.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

From Colin Barker, May 26 2018: (Start)
G.f.: 18*x*(2 + x) / (1  x)^2.
a(n) = 2*a(n1)  a(n2) for n>2.
(End)


MAPLE

seq(54*n18, n = 1..50);


PROG

(PARI) Vec(18*x*(2 + x) / (1  x)^2 + O(x^50)) \\ Colin Barker, May 26 2018
(GAP) List([1..50], n>54*n18); # Muniru A Asiru, May 27 2018


CROSSREFS

Cf. A305069.
Sequence in context: A044174 A044555 A283635 * A182467 A060936 A247246
Adjacent sequences: A305065 A305066 A305067 * A305069 A305070 A305071


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 25 2018


STATUS

approved



