OFFSET
0,3
COMMENTS
T(n,k) is the number of ways to place k rooks in a 3 x n Ferrers board (or diagram) under the Goldman-Haglund i-row creation rook mode for i=2. All row heights are 3.
LINKS
Jay Goldman and James Haglund, Generalized rook polynomials, J. Combin. Theory A 91 (2000), 509-530.
FORMULA
T(n,k) = T(n-1,k) + (k+2) T(n-1,k-1) subject to T(0,0)=1, T(n,k)=0 for n<k and for k<0.
EXAMPLE
The triangle T(n,k) begins in row n=0 with columns 0<=k<=n:
1
1 3
1 6 12
1 9 36 60
1 12 72 240 360
1 15 120 600 1800 2520
1 18 180 1200 5400 15120 20160
1 21 252 2100 12600 52920 141120 181440
1 24 336 3360 25200 141120 564480 1451520 1814400
1 27 432 5040 45360 317520 1693440 6531840 16329600 19958400
CROSSREFS
Cf. A013610 (1-rook coefficients on the 3xn board), A121757 (2-rook coeffs. on the 2xn board), A013609 (1-rook coeffs. on the 2xn board), A013611 (1-rook coeffs. on the 4xn board), A008279 (2-rook coeffs. on the 1xn board), A082030 (row sums?), A049598 (column k=2), A007531 (column k=3 w/o factor 10), A001710 (diagonal?).
KEYWORD
AUTHOR
Ken Joffaniel M. Gonzales, Jan 21 2016
EXTENSIONS
Triangle simplified (reversing rows, offset 0). - R. J. Mathar, May 03 2017
STATUS
approved