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A226493
Closed walks of length n in K_4 graph.
2
0, 12, 24, 84, 240, 732, 2184, 6564, 19680, 59052, 177144, 531444, 1594320, 4782972, 14348904, 43046724, 129140160, 387420492, 1162261464, 3486784404, 10460353200, 31381059612, 94143178824, 282429536484, 847288609440, 2541865828332, 7625597484984, 22876792454964
OFFSET
1,2
COMMENTS
Essentially the same as A218034.
REFERENCES
Mike Krebs and Tony Shaheen, Expander Families and Cayley Graphs, Oxford University Press, Inc. 2011
LINKS
K. Böhmová, C. Dalfó, and C. Huemer, On cyclic Kautz digraphs, Preprint 2016.
Cristina Dalfó, From subKautz digraphs to cyclic Kautz digraphs, arXiv:1709.01882 [math.CO], 2017.
C. Dalfó, The spectra of subKautz and cyclic Kautz digraphs, Linear Algebra and its Applications, 531 (2017), p. 210-219.
Carlos I. Perez-Sanchez, The Spectral Action on quivers, arXiv:2401.03705 [math.RT], 2024.
FORMULA
a(n) = 3*(-1)^n + 3^n = 12*A015518(n-1).
G.f.: 12*x^2 / ( (1+x)*(1-3*x) ). - R. J. Mathar, Jun 29 2013
MATHEMATICA
Table[3 (-1)^k + 3^k, {k, 30}]
PROG
(PARI) a(n) = { 3*(-1)^n + 3^n } \\ Andrew Howroyd, Sep 11 2019
CROSSREFS
Column k=4 of A106512.
Cf. A218034.
Sequence in context: A376436 A109745 A364726 * A371922 A051385 A290304
KEYWORD
nonn,easy
AUTHOR
Gustavo Gordillo, Jun 09 2013
STATUS
approved