A269743 Triangle of generalized Eulerian numbers T(n,k) = _3 read by rows, n >= 1, 0 <= k <= 3*(n-1).

1, 1, 1, 1, 1, 1, 4, 11, 23, 11, 4, 1, 1, 11, 72, 325, 595, 595, 325, 72, 11, 1, 1, 26, 367, 3368, 14679, 34679, 46800, 34679, 14679, 3368, 367, 26, 1, 1, 57, 1630, 28819, 253247, 1212440, 3382133, 5588593, 5588593, 3382133, 1212440, 253247, 28819, 1630, 57, 1

Offset: 1

Author

N. J. A. Sloane, Mar 16 2016

Keywords

• nonn
• tabf

Comments

T(n,k) is the number of nonnegative integer n X n matrices with every row and column sum 3 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

Examples

			Triangle begins:
1,
1,1,1,1,
1,4,11,23,11,4,1,
1,11,72,325,595,595,325,72,11,1,
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..925 (first 25 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

Crossrefs

Row sums are A001500.

Columns k=0..4 are A000012, A000295, A260585, A260727, A260583.

Cf. A008292, A269742, A269744.

Programs

PARI

\\ See link. - Andrew Howroyd, Feb 22 2020

Extensions

Terms a(23) and beyond from Andrew Howroyd, Feb 22 2020