|
|
A216724
|
|
Triangle read by rows: T(n,k) is the number of permutations of [1..n] with k modular progressions of rise 2, distance 1 and length 3 (n >= 0, k >= 0).
|
|
3
|
|
|
1, 1, 2, 3, 3, 24, 0, 100, 15, 0, 5, 594, 108, 18, 0, 4389, 504, 119, 21, 0, 7, 35744, 3520, 960, 64, 32, 0, 325395, 31077, 5238, 927, 207, 27, 0, 9, 3288600, 288300, 42050, 8800, 900, 100, 50, 0, 36489992, 2946141, 409827, 59785, 9174, 1518, 319, 33, 0, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, Congressus Numerantium, Vol. 208 (2011), pp. 147-165.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1
1
2
3 3
24 0
100 15 0 5
594 108 18 0
4389 504 119 21 0 7
35744 3520 960 64 32 0
325395 31077 5238 927 207 27 0 9
3288600 288300 42050 8800 900 100 50 0
...
|
|
MAPLE
|
b:= proc(s, x, y, n) option remember; expand(`if`(s={}, 1, add(
`if`(x>0 and irem(n+x-y, n)=2 and irem(n+y-j, n)=2, z, 1)*
b(s minus {j}, y, j, n), j=s)))
end:
T:= n-> (p-> seq(coeff(p, z, i), i=0..max(0,
iquo(n-1, 2)*2-1)))(b({$1..n}, 0$2, n)):
|
|
MATHEMATICA
|
b[s_, x_, y_, n_] := b[s, x, y, n] = Expand[If[s == {}, 1, Sum[
If[x>0 && Mod[n + x - y, n] == 2 && Mod[n + y - j, n] == 2, z, 1]*
b[s~Complement~{j}, y, j, n], {j, s}]]];
T[n_] := Function[p, Table[Coefficient[p, z, i], {i, 0, Max[0,
Quotient[n - 1, 2]*2 - 1]}]][b[Range[n], 0, 0, n]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|