A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 292, 256, 32, 22, 256, 948, 1723, 1024, 64, 29, 484, 2527, 6454, 10327, 4096, 128, 37, 841, 5913, 18980, 44693, 61996, 16384, 256, 46, 1369, 12577, 49561, 136289, 321163, 371641, 65536, 512, 56, 2116, 24821, 119150

Offset

1,1

Comments

Table starts

....2.......4........7........11.........16..........22..........29..........37

....4......16.......49.......121........256.........484.........841........1369

....8......64......292.......948.......2527........5913.......12577.......24821

...16.....256.....1723......6454......18980.......49561......119150......267643

...32....1024....10327.....44693.....136289......364959......920106.....2218590

...64....4096....61996....321163....1023339.....2715255.....6789502....16634224

..128...16384...371641...2343189....8052573....21347949....51831694...124050234

..256...65536..2227333..17087771...64796052...176196273...418107416...962697852

..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454

.1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

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) = 6*a(n-1) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6)

k=4: [order 23]

k=5: [order 93]

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) = polynomial of degree 6 for n>1

n=4: a(n) = polynomial of degree 8 for n>6

n=5: a(n) = polynomial of degree 10 for n>12

n=6: a(n) = polynomial of degree 12 for n>20

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A000302

Column 3 is A188748

Row 1 is A000124

Row 2 is A086601

Sequence in context: A181224 A188567 A262274 * A223680 A189264 A188992

Adjacent sequences: A223666 A223667 A223668 * A223670 A223671 A223672

Keyword

nonn,tabl

Author

R. H. Hardin Mar 25 2013

Status

approved