OFFSET
1,1
COMMENTS
a(n) provides the number of vertices in the HcDN1(n) network (see Fig. 3 in the Hayat et al. paper).
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 Journal for Information Science and Technology, Volume 18, Number 2, 2015, pages 144-165.
Leo Tavares, Illustration: Hexagonal Square Rays
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Bruno Berselli, May 10 2018: (Start)
O.g.f.: x*(7 + 10*x + x^2)/(1 - x)^3.
E.g.f.: -1 + (1 + 3*x)^2*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
EXAMPLE
From Andrew Howroyd, May 09 2018: (Start)
Illustration of the order 1 graph:
o---o
/ \ / \
o---o---o
\ / \ /
o---o
The order 2 graph is composed of 7 such hexagons and in general the HcDN1(n) graph is constructed from a honeycomb graph with each hexagon subdivided into triangles.
(End)
MAPLE
seq(9*n^2-3*n+1, n = 1 .. 40);
PROG
(PARI) a(n) = 9*n^2-3*n+1; \\ Altug Alkan, May 09 2018
(PARI) Vec(x*(7 + 10*x + x^2)/(1 - x)^3 + O(x^40)) \\ Colin Barker, May 23 2018
(Julia) [9*n^2-3*n+1 for n in 1:40] |> println # Bruno Berselli, May 10 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved