|
|
A329550
|
|
Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].
|
|
2
|
|
|
0, 0, 0, 2, 16, 108, 864, 7200, 69120, 705600, 8064000, 97977600, 1306368000, 18441561600, 281652940800, 4533271142400, 78111748915200, 1412288317440000, 27115935694848000, 544201764986880000, 11524272670310400000, 254238259854458880000, 5887622859787468800000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
All terms are even.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k>=1} k * A152877(n,k).
|
|
EXAMPLE
|
a(3) = 2: 123, 321.
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n<5, [0$3, 2, 16][n+1],
(n-2)*(2*(n-4)*a(n-1)+(n-3)^2*n*a(n-2))/(n-3)/(n-4))
end:
seq(a(n), n=0..30);
|
|
MATHEMATICA
|
a[n_] := a[n] = If[n < 5, {0, 0, 0, 2, 16}[[n+1]],
(n-2)*(2*(n-4)*a[n-1] + (n-3)^2*n*a[n-2])/(n-3)/(n-4)];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|