A223680 T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal.

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 316, 256, 32, 22, 256, 1118, 2032, 1024, 64, 29, 484, 3177, 9822, 13045, 4096, 128, 37, 841, 7745, 35509, 85663, 83737, 16384, 256, 46, 1369, 16857, 105995, 384009, 744272, 537496, 65536, 512, 56, 2116, 33615, 275775

Offset: 1

Author

R. H. Hardin Mar 25 2013

Keywords

• nonn
• tabl

Comments

Table starts

....2.......4.........7.........11..........16...........22............29

....4......16........49........121.........256..........484...........841

....8......64.......316.......1118........3177.........7745.........16857

...16.....256......2032.......9822.......35509.......105995........275775

...32....1024.....13045......85663......384009......1363639.......4123210

...64....4096.....83737.....744272.....4106403.....17068664......58944337

..128...16384....537496....6458585....43632367....210660192.....821284360

..256...65536...3450100...56030742...462307835...2577807779...11265254628

..512..262144..22145617..486038270..4893189359..31402790284..152970187735

.1024.1048576.142149013.4215998078.51766786082.381690187059.2064772010660

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..480

Crossrefs

Column 1 is A000079

Column 2 is A000302

Column 3 is A188868

Row 1 is A000124

Row 2 is A086601

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1)

k=3: a(n) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4)

k=4: [order 9]

k=5: [order 19]

k=6: [order 36]

k=7: [order 70]

Empirical for row n:

n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1

n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1

n=3: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1

n=4: polynomial of degree 8

n=5: polynomial of degree 10 for n>2

n=6: polynomial of degree 12 for n>3

n=7: polynomial of degree 14 for n>4