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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 (list; graph; refs; listen; history; text; internal format)
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: A120356 A109745 A364726 * A051385 A290304 A289335
KEYWORD
nonn,easy
AUTHOR
Gustavo Gordillo, Jun 09 2013
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)