

A304619


a(n) = 324*n^2  804*n + 468 (n>=2).


2



156, 972, 2436, 4548, 7308, 10716, 14772, 19476, 24828, 30828, 37476, 44772, 52716, 61308, 70548, 80436, 90972, 102156, 113988, 126468, 139596, 153372, 167796, 182868, 198588, 214956, 231972, 249636, 267948, 286908, 306516, 326772, 347676, 369228, 391428, 414276, 437772, 461916, 486708
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OFFSET

2,1


COMMENTS

For n>=3, a(n) is the second Zagreb index of the hexagonal network HX(n).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The Mpolynomial of the hexagonal network HX(n) is M(HX(n); x,y) = 12*x^3*y^4 + 6*x^3*y^6 + 6*(n3)*x^4*y^4 + 12*(n2)*x^4*y^6 + (9*n^233*n+30)*x^6*y^6.
9*a(n) + 277 is a square.  Bruno Berselli, May 18 2018


LINKS

Colin Barker, Table of n, a(n) for n = 2..1000
S. Hayat and M. Imran, Computation of topological indices of certain networks, Applied Mathematics and Computation, 240, 2014, 213228/
M. N. Husin and R. Hasni, More results on computation of topological indices of certain networks, Int. J. Networking and Virtual Organisations, 17, No. 1, 2017, 4663.
B. Rajan , A. William, C. Grigorius, and S. Stephen, On certain topological indices of silicate, honeycomb and hexagonal networks, J. Comp. & Math. Sci., 3, No. 5, 2012, 530535.
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 (3,3,1).


FORMULA

From Colin Barker, May 18 2018: (Start)
G.f.: 12*x^2*(13 + 42*x  x^2) / (1  x)^3.
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n>4.
(End)


MAPLE

seq(468804*n+324*n^2, n = 2..40);


PROG

(GAP) List([2..40], n>324*n^2804*n+468); # Muniru A Asiru, May 18 2018
(PARI) a(n) = 324*n^2  804*n + 468; \\ Altug Alkan, May 18 2018
(PARI) Vec(12*x^2*(13 + 42*x  x^2) / (1  x)^3 + O(x^40)) \\ Colin Barker, May 18 2018


CROSSREFS

Cf. A304618.
Sequence in context: A038476 A158550 A156994 * A204718 A232718 A204957
Adjacent sequences: A304616 A304617 A304618 * A304620 A304621 A304622


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 17 2018


STATUS

approved



