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

Author

R. H. Hardin Mar 27 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000244

Column 2 is A001019

Row 1 is A223718

Row 2 is A223719

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