A304164 a(n) = 27*n^2 - 21*n + 6 (n>=1).

12, 72, 186, 354, 576, 852, 1182, 1566, 2004, 2496, 3042, 3642, 4296, 5004, 5766, 6582, 7452, 8376, 9354, 10386, 11472, 12612, 13806, 15054, 16356, 17712, 19122, 20586, 22104, 23676, 25302, 26982, 28716, 30504, 32346, 34242, 36192, 38196, 40254, 42366

Offset

1,1

Comments

a(n) is the number of edges in the HcDN1(n) network (see Fig. 3 in the Hayat et al. manuscript).

Links

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

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.: 6*x*(2 + 6*x + 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.: 3*exp(x)*(2 + 2*x + 9*x^2) - 6. - Stefano Spezia, Apr 15 2023

Maple

seq(27*n^2-21*n+6, n = 1 .. 40);

Prog

(PARI) a(n) = 27*n^2-21*n+6; \\ Altug Alkan, May 09 2018
(PARI) Vec(6*x*(2 + 6*x + x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, May 10 2018
(GAP) List([1..40], n->27*n^2-21*n+6); # Muniru A Asiru, May 10 2018

Crossrefs

Cf. A304163.

Sequence in context: A101523 A340302 A143698 * A199531 A188660 A047928

Adjacent sequences: A304161 A304162 A304163 * A304165 A304166 A304167

Keyword

nonn,easy

Author

Emeric Deutsch, May 09 2018

Status

approved