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A304164
a(n) = 27*n^2 - 21*n + 6 (n>=1).
4
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
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.
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
Cf. A304163.
Sequence in context: A101523 A340302 A143698 * A199531 A374374 A188660
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 09 2018
STATUS
approved