A223789 T(n,k)=Number of nXk 0..2 arrays with rows, diagonals and antidiagonals unimodal

3, 9, 9, 22, 81, 27, 46, 484, 729, 81, 86, 2116, 8635, 6561, 243, 148, 7396, 62365, 151580, 59049, 729, 239, 21904, 334230, 1560013, 2703137, 531441, 2187, 367, 57121, 1455816, 11012718, 39387861, 48302789, 4782969, 6561, 541, 134689, 5425943

Offset

1,1

Comments

Table starts

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

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

....27........729..........8635...........62365............334230

....81.......6561........151580.........1560013..........11012718

...243......59049.......2703137........39387861.........343454446

...729.....531441......48302789......1026135371.......11150023974

..2187....4782969.....862007289.....27088106846......377163884938

..6561...43046721...15379566078....715394830136....12972494260444

.19683..387420489..274427327200..18858304684055...446829906314726

.59049.3486784401.4896915028511.496722962933967.15355124632228358

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 9*a(n-1)

k=3: [order 15]

k=4: [order 80]

Empirical: rows n=1..5 are polynomials of order 4*n for k>0,0,1,8,15

Example

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

Crossrefs

Column 1 is A000244

Column 2 is A001019

Row 1 is A223718

Row 2 is A223719

Sequence in context: A223831 A223885 A223892 * A223975 A226852 A207235

Adjacent sequences: A223786 A223787 A223788 * A223790 A223791 A223792

Keyword

nonn,tabl

Author

R. H. Hardin Mar 27 2013

Status

approved