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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A000302

Column 3 is A188868

Row 1 is A000124

Row 2 is A086601

Sequence in context: A188567 A262274 A223669 * A189264 A188992 A189617

Adjacent sequences: A223677 A223678 A223679 * A223681 A223682 A223683

Keyword

nonn,tabl

Author

R. H. Hardin Mar 25 2013

Status

approved