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%I #19 Oct 20 2024 09:40:25
%S 1,3,12,39,126,381,1169,3528,10611,31869,95742,287235,861753,2585646,
%T 7757199,23270967,69814035,209444148,628329001,1884986319,5654972973,
%U 16964909958,50894701155,152684163435,458052522680,1374157361943,4122472203369,12367417119426,37102250507967,111306750857883,333920255806104,1001760766199415,3005282290140126
%N Coefficients in expansion of graph zeta function of graph obtained by adding 4 vertices to each edge of K_5.
%H Vincenzo Librandi, <a href="/A240806/b240806.txt">Table of n, a(n) for n = 0..1000</a>
%H Horton, Matthew D., H. M. Stark, and Audrey A. Terras. <a href="http://math.ucsd.edu/~aterras/snowbird.pdf">What are zeta functions of graphs and what are they good for?</a> Contemporary Mathematics 415 (2006): 173-190. The graph is shown on the left in Fig. 1.
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, -6, -9, -15, 35, 60, -75, -75, 81, 42, -43, -9, 9).
%F G.f.: 1/(-(1-x)^6*(x+1)^5*(9*x^3+2*x-1)). - _Vincenzo Librandi_, Apr 16 2014
%F 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
%e The zeta function is 1/((1-x^10)^5*(1-3*x^5)*(1-x^5)*(1+x^5+3*x^10)).
%t CoefficientList[Series[1/(-(1 - x)^6 (x + 1)^5 (9 x^3 + 2 x - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Apr 16 2014 *)
%Y Cf. A240805.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Apr 15 2014