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%I #11 May 17 2023 12:25:34
%S 0,2,3,6,12,24,44,84,159,300,564,1064,2004,3774,7107,13386,25208,
%T 47472,89400,168360,317055,597080,1124424,2117520,3987720,7509690,
%U 14142275,26632782,50154948,94451976,177872292,334969724,630816159,1187955204,2237161404
%N Number of permutations of [n] with no fixed points where the maximal displacement of an element equals two.
%H Alois P. Heinz, <a href="/A321048/b321048.txt">Table of n, a(n) for n = 2..2000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,-2,1).
%F G.f.: (x-2)*x^3/((x-1)*(x+1)*(x^4-2*x^3+x^2-2*x+1)).
%F a(n) = A033305(n) - A059841(n).
%F a(n) = 2*a(n-1) - 2*a(n-5) + a(n-6). - _Wesley Ivan Hurt_, May 17 2023
%Y Column k=2 of A259784.
%Y Cf. A059841, A033305.
%K nonn,easy
%O 2,2
%A _Alois P. Heinz_, Oct 26 2018
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