A240806 Coefficients in expansion of graph zeta function of graph obtained by adding 4 vertices to each edge of K_5.

1, 3, 12, 39, 126, 381, 1169, 3528, 10611, 31869, 95742, 287235, 861753, 2585646, 7757199, 23270967, 69814035, 209444148, 628329001, 1884986319, 5654972973, 16964909958, 50894701155, 152684163435, 458052522680, 1374157361943, 4122472203369, 12367417119426, 37102250507967, 111306750857883, 333920255806104, 1001760766199415, 3005282290140126

Offset

0,2

Links

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

Horton, Matthew D., H. M. Stark, and Audrey A. Terras. What are zeta functions of graphs and what are they good for? Contemporary Mathematics 415 (2006): 173-190. The graph is shown on the left in Fig. 1.

Index entries for linear recurrences with constant coefficients, signature (3, 3, -6, -9, -15, 35, 60, -75, -75, 81, 42, -43, -9, 9).

Formula

G.f.: 1/(-(1-x)^6*(x+1)^5*(9*x^3+2*x-1)). - Vincenzo Librandi, Apr 16 2014

a(n) = 3*a(n-1) + 3*a(n-2) - 6*a(n-3) - 9*a(n-4) - 15*a(n-5) + 35*a(n-6) + 60*a(n-7) - 75*a(n-8) - 75*a(n-9) + 81*a(n-10) + 42*a(n-11) - 43*a(n-12) - 9*a(n-13) + 9*a(n-14) for n > 13. - Chai Wah Wu, Jan 19 2020

Example

The zeta function is 1/((1-x^10)^5*(1-3*x^5)*(1-x^5)*(1+x^5+3*x^10)).

Mathematica

CoefficientList[Series[1/(-(1 - x)^6 (x + 1)^5 (9 x^3 + 2 x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 16 2014 *)

Crossrefs

Cf. A240805.

Sequence in context: A055294 A029858 A123109 * A242587 A330169 A375256

Adjacent sequences: A240803 A240804 A240805 * A240807 A240808 A240809

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 15 2014

Status

approved