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A269743
Triangle of generalized Eulerian numbers T(n,k) = <n,k>_3 read by rows, n >= 1, 0 <= k <= 3*(n-1).
5
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
1,7
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
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
EXAMPLE
Triangle begins:
1,
1,1,1,1,
1,4,11,23,11,4,1,
1,11,72,325,595,595,325,72,11,1,
...
PROG
(PARI) \\ See link. - Andrew Howroyd, Feb 22 2020
CROSSREFS
Row sums are A001500.
Columns k=0..4 are A000012, A000295, A260585, A260727, A260583.
Sequence in context: A174405 A016274 A092656 * A298790 A038435 A038442
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Mar 16 2016
EXTENSIONS
Terms a(23) and beyond from Andrew Howroyd, Feb 22 2020
STATUS
approved