A240805 Coefficients in expansion of graph zeta function for complete graph K_4.

1, 0, 0, 8, 6, 0, 48, 72, 39, 272, 600, 624, 1772, 4416, 6528, 13488, 32157, 57504, 110064, 241848, 471618, 905280, 1880112, 3773112, 7371427, 14901552, 30032904, 59457632, 119043912, 239326080, 477043584, 953016288, 1910769273, 3818911040, 7630062048, 15274147560, 30550681406, 61067895168, 122165728944, 244373547432

Offset

0,4

References

Audrey Terras, Zeta functions of graphs. A stroll through the garden. Cambridge Studies in Advanced Mathematics, 128. Cambridge University Press, Cambridge, 2011. xii+239 pp. ISBN: 978-0-521-11367-0; MR2768284 (2012d:05016).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

L. Bartholdi, Review of Terras (2011), Bull. Amer. Math. Soc., 51 (2014), 177-185.

Index entries for linear recurrences with constant coefficients, signature (0,0,8,6,0,-16,-24,3,16,24,0,-16).

Formula

From Chai Wah Wu, Jan 19 2020: (Start)

a(n) = 8*a(n-3) + 6*a(n-4) - 16*a(n-6) - 24*a(n-7) + 3*a(n-8) + 16*a(n-9) + 24*a(n-10) - 16*a(n-12) for n > 11.

G.f.: 1/((x - 1)^3*(x + 1)^2*(2*x - 1)*(2*x^2 + x + 1)^3). (End)

Example

Zeta function is 1/((1-x^2)^2*(1-x)*(1-2*x)*(1+x+2*x^2)^3).

Mathematica

CoefficientList[Series[1/((1 - x^2)^2 (1 - x) (1 - 2 x) (1 + x + 2 x^2)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 16 2014 *)
LinearRecurrence[{0, 0, 8, 6, 0, -16, -24, 3, 16, 24, 0, -16}, {1, 0, 0, 8, 6, 0, 48, 72, 39, 272, 600, 624}, 40] (* Harvey P. Dale, Oct 19 2024 *)

Crossrefs

Cf. A240806.

Sequence in context: A156551 A074738 A344041 * A010115 A268438 A329090

Adjacent sequences: A240802 A240803 A240804 * A240806 A240807 A240808

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 15 2014

Status

approved