%I #9 Jan 20 2024 15:39:55
%S 1,2,4,8,16,29,51,83,131,196,286,402,554,743,981,1269,1621,2038,2536,
%T 3116,3796,4577,5479,6503,7671,8984,10466,12118,13966,16011,18281,
%U 20777,23529,26538,29836,33424,37336,41573,46171,51131,56491,62252,68454,75098
%N Number of (3412,1234)-avoiding involutions in S_n.
%H E. S. Egge, <a href="http://arXiv.org/abs/math.CO/0307050">Restricted 3412-Avoiding Involutions: Continued Fractions, Chebyshev Polynomials and Enumerations</a>, sec. 8
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F a(n) = (2*n^4-4*n^3+28*n^2-2*n+81-6*n*(-1)^n+15*(-1)^n)/96.
%F G.f.: -x*(x^6-2*x^5+x^4+3*x^3-x^2-x+1) / ((x-1)^5*(x+1)^2). - _Colin Barker_, Jul 16 2013
%F a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7). - _Wesley Ivan Hurt_, Jan 20 2024
%t CoefficientList[Series[-(x^6 - 2*x^5 + x^4 + 3*x^3 - x^2 - x + 1)/((x - 1)^5*(x + 1)^2), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jan 20 2024 *)
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Jul 06 2003
%E More terms from _Colin Barker_, Jul 16 2013
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