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%I #42 Jan 11 2024 11:58:53
%S 0,12,24,84,240,732,2184,6564,19680,59052,177144,531444,1594320,
%T 4782972,14348904,43046724,129140160,387420492,1162261464,3486784404,
%U 10460353200,31381059612,94143178824,282429536484,847288609440,2541865828332,7625597484984,22876792454964
%N Closed walks of length n in K_4 graph.
%C Essentially the same as A218034.
%D Mike Krebs and Tony Shaheen, Expander Families and Cayley Graphs, Oxford University Press, Inc. 2011
%H K. Böhmová, C. Dalfó, and C. Huemer, <a href="http://upcommons.upc.edu/bitstream/handle/2117/80848/Kautz-subdigraphs.pdf">On cyclic Kautz digraphs</a>, Preprint 2016.
%H Cristina Dalfó, <a href="https://arxiv.org/abs/1709.01882">From subKautz digraphs to cyclic Kautz digraphs</a>, arXiv:1709.01882 [math.CO], 2017.
%H C. Dalfó, <a href="https://dx.doi.org/10.1016/j.laa.2017.05.046">The spectra of subKautz and cyclic Kautz digraphs</a>, Linear Algebra and its Applications, 531 (2017), p. 210-219.
%H Carlos I. Perez-Sanchez, <a href="https://arxiv.org/abs/2401.03705">The Spectral Action on quivers</a>, arXiv:2401.03705 [math.RT], 2024.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F a(n) = 3*(-1)^n + 3^n = 12*A015518(n-1).
%F G.f.: 12*x^2 / ( (1+x)*(1-3*x) ). - _R. J. Mathar_, Jun 29 2013
%t Table[3 (-1)^k + 3^k, {k, 30}]
%o (PARI) a(n) = { 3*(-1)^n + 3^n } \\ _Andrew Howroyd_, Sep 11 2019
%Y Column k=4 of A106512.
%Y Cf. A218034.
%K nonn,easy
%O 1,2
%A _Gustavo Gordillo_, Jun 09 2013
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