|
%I #26 Feb 19 2024 12:10:23
%S 1,9,51,235,966,3702,13546,47994,166095,564679,1893285,6277677,
%T 20626588,67260540,217924068,702199684,2251881645,7191492885,
%U 22882022695,72568700415,229473998466,723725687314,2277088137966,7148997642270,22400192612251,70060176893427
%N Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(4,0,-,0)(x).
%H Vincenzo Librandi, <a href="/A213164/b213164.txt">Table of n, a(n) for n = 5..1000</a>
%H S. Kitaev, J. Remmel and M. Tiefenbruck, <a href="http://arxiv.org/abs/1201.6243">Marked mesh patterns in 132-avoiding permutations I</a>, arXiv preprint arXiv:1201.6243 [math.CO], 2012-2014.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,46,-33,9).
%F From _Vaclav Kotesovec_, Nov 25 2012: (Start)
%F a(n) = ((2*n-11)*3^(n-2)+2*n^2-2*n+3)/16
%F Recurrence: a(n) = 9*a(n-1) - 30*a(n-2) + 46*a(n-3) - 33*a(n-4) + 9*a(n-5)
%F G.f.: -((1-9*x+30*x^2-46*x^3+33*x^4)/(9*(-1+x)^3*(-1+3*x)^2))
%F (End)
%t CCC[t] = (1 - (1 - 4*t)^(1/2))/(2*t); NQ0[t, x] = ((1 + t - t*x) - ((1 + t - t*x)^2 - 4*t)^(1/2))/(2*t); NQ1[t, x] = 1/(1 - t*NQ0[t, x]); NQ2[t, x] = 1/(1 - t*NQ1[t, x]); NQ3[t, x] = 1/(1 - t*NQ2[t, x]); NQ4[t, x] = 1/(1 - t*NQ3[t, x]); CoefficientList[Coefficient[Simplify[Series[NQ4[t, x], {t, 0, 20}]], x], t] (* Robert Price, Jun 06 2012 *)
%t LinearRecurrence[{9, -30, 46, -33, 9}, {1, 9, 51, 235, 966}, 50] (* _Vincenzo Librandi_, Nov 25 2012 *)
%o (Magma) I:=[1, 9, 51, 235, 966]; [n le 5 select I[n] else 9*Self(n-1) - 30*Self(n-2)+ 46*Self(n-3) - 33*Self(n-4) + 9*Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Nov 25 2012
%K nonn
%O 5,2
%A _Robert Price_, Jun 06 2012
|
