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);
MATHEMATICA
Table[27n^2-21n+6, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {12, 72, 186}, 40] (* Harvey P. Dale, Aug 31 2024 *)
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved