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

Author

Gustavo Gordillo, Jun 09 2013

Keywords

• nonn
• easy

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

Crossrefs

Column k=4 of A106512.

Cf. A218034.

Programs

Mathematica

Table[3 (-1)^k + 3^k, {k, 30}]

PARI

a(n) = { 3*(-1)^n + 3^n } \\ Andrew Howroyd, Sep 11 2019

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