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A317283 Number of permutations of [n] with exactly three increasing runs of even length.

%I A317283 #4 Jul 25 2018 16:55:03
%S A317283 61,906,8965,94398,1088575,12625694,150890533,1914036434,25485825638,
%T A317283 353702731940,5141233861254,78259458749608,1243051438276365,
%U A317283 20579839942072222,354951501710697119,6367683567830126402,118640486378324764141,2293339890430027143606
%N A317283 Number of permutations of [n] with exactly three increasing runs of even length.
%H A317283 Alois P. Heinz, <a href="/A317283/b317283.txt">Table of n, a(n) for n = 6..472</a>
%p A317283 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317283       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317283       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 4)
%p A317283     end:
%p A317283 a:= n-> coeff(b(n, 0$2), x, 3):
%p A317283 seq(a(n), n=6..30);
%Y A317283 Column k=3 of A097592.
%K A317283 nonn
%O A317283 6,1
%A A317283 _Alois P. Heinz_, Jul 25 2018