OFFSET
1,6
COMMENTS
T(n,k) is the number of nonnegative integer n X n matrices with every row and column sum 2 and sum of entries below the main diagonal k. The case when every row and column sum is 1 is given by the Eulerian numbers (A008292). - Andrew Howroyd, Feb 22 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1600 (first 40 rows)
Esther M. Banaian, Generalized Eulerian Numbers and Multiplex Juggling Sequences, (2016). All College Thesis Program. Paper 24.
E. Banaian, S. Butler, C. Cox, J. Davis, J. Landgraf and S. Ponce, A generalization of Eulerian numbers via rook placements, arXiv:1508.03673 [math.CO], 2015.
Andrew Howroyd, PARI Program
EXAMPLE
Triangle begins:
1;
1, 1, 1;
1, 4, 11, 4, 1;
1, 11, 72, 114, 72, 11, 1;
1, 26, 367, 1492, 2438, 1492, 367, 26, 1;
1, 57, 1630, 13992, 48965, 73120, 48965, 13992, 1630, 57, 1;
...
The matrices for row n=3, k=0..2 are:
[2 0] [1 1] [0 2]
[0 2] [1 1] [2 0]
PROG
(PARI) \\ See link. - Andrew Howroyd, Feb 22 2020
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Mar 16 2016
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, Feb 22 2020
STATUS
approved