A223975 T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal

3, 9, 9, 22, 81, 27, 46, 484, 729, 81, 86, 2116, 9515, 6561, 243, 148, 7396, 76092, 186004, 59049, 729, 239, 21904, 440628, 2558848, 3628696, 531441, 2187, 367, 57121, 2026448, 22935921, 84988435, 70779056, 4782969, 6561, 541, 134689, 7829639

Offset

1,1

Comments

Table starts

.....3..........9.............22...............46.................86

.....9.........81............484.............2116...............7396

....27........729...........9515............76092.............440628

....81.......6561.........186004..........2558848...........22935921

...243......59049........3628696.........84988435.........1140963027

...729.....531441.......70779056.......2809740785........55803232969

..2187....4782969.....1380511272......92756321858......2708281019793

..6561...43046721....26926081924....3060966419662....131014406127439

.19683..387420489...525177301935..100999995564503...6329626912147424

.59049.3486784401.10243271456697.3332485315028073.305632588672082728

Links

R. H. Hardin, Table of n, a(n) for n = 1..286

Formula

Empirical: columns k=1..6 have recurrences of order 1,1,7,18,43,91

Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,0,0,2,3,4

Example

Some solutions for n=3 k=4
..0..2..0..0....1..2..2..1....2..1..1..0....1..2..2..0....0..0..0..0
..0..1..2..1....0..0..1..1....1..2..2..2....0..2..1..0....0..2..2..0
..0..1..2..2....0..1..0..0....0..1..1..2....1..1..0..0....0..2..1..1

Crossrefs

Column 1 is A000244

Column 2 is A001019

Row 1 is A223718

Row 2 is A223719

Sequence in context: A223885 A223892 A223789 * A226852 A207235 A207228

Adjacent sequences: A223972 A223973 A223974 * A223976 A223977 A223978

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved