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

Author

R. H. Hardin Mar 25 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079

Column 2 is A000302

Column 3 is A188748

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) = 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