A226493 Closed walks of length n in K_4 graph.

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

Table of n, a(n) for n=1..28.

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.

Index entries for linear recurrences with constant coefficients, signature (2,3).

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

Adjacent sequences: A226490 A226491 A226492 * A226494 A226495 A226496

Keyword

nonn,easy

Author

Gustavo Gordillo, Jun 09 2013

Status

approved