A329550 - OEIS

%I #16 Apr 21 2022 05:24:55

%S 0,0,0,2,16,108,864,7200,69120,705600,8064000,97977600,1306368000,

%T 18441561600,281652940800,4533271142400,78111748915200,

%U 1412288317440000,27115935694848000,544201764986880000,11524272670310400000,254238259854458880000,5887622859787468800000

%N Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].

%C All terms are even.

%H Alois P. Heinz, <a href="/A329550/b329550.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = Sum_{k>=1} k * A152877(n,k).

%F a(n) ~ n! * n / 4. - _Vaclav Kotesovec_, Nov 19 2019

%e a(3) = 2: 123, 321.

%p a:= proc(n) option remember; `if`(n<5, [0$3, 2, 16][n+1],

%p      (n-2)*(2*(n-4)*a(n-1)+(n-3)^2*n*a(n-2))/(n-3)/(n-4))

%p     end:

%p seq(a(n), n=0..30);

%t a[n_] := a[n] = If[n < 5, {0, 0, 0, 2, 16}[[n+1]],

%t      (n-2)*(2*(n-4)*a[n-1] + (n-3)^2*n*a[n-2])/(n-3)/(n-4)];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 21 2022, after _Alois P. Heinz_ *)

%Y Cf. A152877.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Nov 16 2019