A221879 Triangle T(n,k) read by rows: Number of order-reversing full contraction mappings (of an n-chain) with 1 fixed point and height exactly k.

1, 2, 0, 3, 2, 1, 4, 6, 4, 0, 5, 12, 12, 4, 1, 6, 20, 28, 18, 6, 0, 7, 30, 55, 52, 27, 6, 1, 8, 42, 96, 120, 88, 36, 8, 0, 9, 56, 154, 240, 230, 136, 48, 8, 1, 10, 72, 232, 434, 516, 400, 200, 60, 10, 0, 11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1

Offset

1,2

Comments

Row sums are A059570.

References

A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted).

Links

Table of n, a(n) for n=1..66.

Formula

T(n, 1) = 1, T(2,2) = 0 and T(n,k) = (n-k+1)*C(n-2,k-1) + T(n-2,k-2) for k > 0.

Example

T (4,6) = 6 because there are exactly 6 order-reversing full contraction mappings (of a 4-chain) with 1 fixed point and of height exactly 2, namely: (3222), (2221), (2211), (4433), (4333), (3332).
Triangle starts
1,
2, 0,
3, 2, 1,
4, 6, 4, 0,
5, 12, 12, 4, 1,
6, 20, 28, 18, 6, 0,
7, 30, 55, 52, 27, 6, 1,
8, 42, 96, 120, 88, 36, 8, 0,
9, 56, 154, 240, 230, 136, 48, 8, 1,
10, 72, 232, 434, 516, 400, 200, 60, 10, 0,
11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1
...

Crossrefs

Cf. A059570, A221876, A221877, A221878, A221880, A221881, A221882.

Sequence in context: A241556 A242029 A090722 * A171934 A303205 A082785

Adjacent sequences: A221876 A221877 A221878 * A221880 A221881 A221882

Keyword

nonn,tabl

Author

Abdullahi Umar, Feb 28 2013

Status

approved