A221879 - OEIS

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

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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

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

...