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%I #25 Apr 16 2023 08:36:43
%S 12,72,186,354,576,852,1182,1566,2004,2496,3042,3642,4296,5004,5766,
%T 6582,7452,8376,9354,10386,11472,12612,13806,15054,16356,17712,19122,
%U 20586,22104,23676,25302,26982,28716,30504,32346,34242,36192,38196,40254,42366
%N a(n) = 27*n^2 - 21*n + 6 (n>=1).
%C a(n) is the number of edges in the HcDN1(n) network (see Fig. 3 in the Hayat et al. manuscript).
%H Colin Barker, <a href="/A304164/b304164.txt">Table of n, a(n) for n = 1..1000</a>
%H S. Hayat, M. A. Malik, and M. Imran, <a href="http://www.romjist.ro/content/pdf/03-mimran.pdf">Computing topological indices of honeycomb derived networks</a>, Romanian J. of Information Science and Technology, 18, No. 2, 2015, 144-165.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Colin Barker_, May 10 2018: (Start)
%F G.f.: 6*x*(2 + 6*x + x^2)/(1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%F E.g.f.: 3*exp(x)*(2 + 2*x + 9*x^2) - 6. - _Stefano Spezia_, Apr 15 2023
%p seq(27*n^2-21*n+6, n = 1 .. 40);
%o (PARI) a(n) = 27*n^2-21*n+6; \\ _Altug Alkan_, May 09 2018
%o (PARI) Vec(6*x*(2 + 6*x + x^2) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, May 10 2018
%o (GAP) List([1..40],n->27*n^2-21*n+6); # _Muniru A Asiru_, May 10 2018
%Y Cf. A304163.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 09 2018
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