A304166 a(n) = 972*n^2 - 1224*n + 414 with n > 0.

162, 1854, 5490, 11070, 18594, 28062, 39474, 52830, 68130, 85374, 104562, 125694, 148770, 173790, 200754, 229662, 260514, 293310, 328050, 364734, 403362, 443934, 486450, 530910, 577314, 625662, 675954, 728190, 782370, 838494, 896562, 956574, 1018530, 1082430, 1148274, 1216062, 1285794, 1357470, 1431090, 1506654

Offset

1,1

Comments

a(n) provides the second Zagreb index of the HcDN1(n) network (see Fig. 3 in the Hayat et al. paper).

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 M-polynomial of HcDN1(n) is M(HcDN1(n); x,y) = 6x^3*y^3 + 12(n-1)x^3*y^5 + 6nx^3*y^6 + 18(n-1)x^5*y^6 + (27n^2 - 57n + 30)x^6*y^6. - Emeric Deutsch, May 11 2018

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Emeric Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

S. Hayat, M. A. Malik, and M. Imran, Computing topological indices of honeycomb derived networks, Romanian J. of Information Science and Technology, 18, No. 2, 2015, 144-165.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, May 10 2018: (Start)

G.f.: 18*x*(9 + 76*x + 23*x^2)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

E.g.f.: 18*(exp(x)*(23 - 14*x + 54*x^2) - 23). - Stefano Spezia, Apr 15 2023

Maple

seq(972*n^2-1224*n+414, n = 1 .. 40);

Prog

(PARI) a(n) = 972*n^2-1224*n+414; \\ Altug Alkan, May 09 2018
(PARI) Vec(18*x*(9 + 76*x + 23*x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, May 10 2018

Crossrefs

Cf. A304163, A304164, A304165.

Sequence in context: A302731 A206145 A342850 * A213288 A302532 A288489

Adjacent sequences: A304163 A304164 A304165 * A304167 A304168 A304169

Keyword

nonn,easy

Author

Emeric Deutsch, May 09 2018

Status

approved