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A188899 Third row of array in A187617.

%I A188899 #31 Jan 10 2021 14:32:45
%S A188899 1,5,36,281,2245,18061,145601,1174500,9475901,76455961,616891945,
%T A188899 4977472781,40161441636,324048393905,2614631600701,21096536145301,
%U A188899 170220478472105,1373448758774436,11081871650713781,89415697915538545,721463601671126161,5821234309893001301,46969478172465070500,378980086070257592201,3057856106268358639861
%N A188899 Third row of array in A187617.
%H A188899 Alois P. Heinz, <a href="/A188899/b188899.txt">Table of n, a(n) for n = 0..400</a>
%H A188899 N. Allegra, <a href="http://arxiv.org/abs/1410.4131">Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics</a>, arXiv:1410.4131 [cond-mat.stat-mech], 2014. See Table 1.
%H A188899 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-25,11,-1).
%F A188899 G.f.: (1-x)*(x^2-5*x+1)/(x^4-11*x^3+25*x^2-11*x+1). - _Alois P. Heinz_, Oct 28 2012
%p A188899 ft:=(m,n)->
%p A188899 2^(m*n/2)*mul( mul(
%p A188899 (cos(Pi*i/(n+1))^2+cos(Pi*j/(m+1))^2), j=1..m/2), i=1..n/2);
%p A188899 gt:=(m,n)->round(evalf(ft(m,n),300));
%p A188899 tt:=[seq(gt(4,2*n),n=0..10)];
%p A188899 # second Maple program:
%p A188899 a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|11|-25|11>>^n.
%p A188899         <<1, 5, 36, 281>>)[1, 1]:
%p A188899 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 28 2012
%t A188899 LinearRecurrence[{11, -25, 11, -1}, {1, 5, 36, 281}, 25] (* _Jean-François Alcover_, Jun 17 2018 *)
%o A188899 (PARI) x='x+O('x^200); Vec((1-x)*(x^2-5*x+1)/(x^4-11*x^3+25*x^2-11*x+1)) \\ _Altug Alkan_, Mar 23 2016
%Y A188899 Bisection (odd part) of A005178. - _Alois P. Heinz_, Oct 28 2012
%K A188899 nonn
%O A188899 0,2
%A A188899 _N. J. A. Sloane_, Apr 13 2011