A235679 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise.

16, 58, 58, 208, 380, 208, 742, 2456, 2456, 742, 2644, 15790, 28584, 15790, 2644, 9418, 101398, 330840, 330840, 101398, 9418, 33544, 650928, 3824528, 6894210, 3824528, 650928, 33544, 119470, 4178316, 44196144, 143484144, 143484144, 44196144

Offset

1,1

Comments

Table starts

......16.........58..........208.............742...............2644

......58........380.........2456...........15790.............101398

.....208.......2456........28584..........330840............3824528

.....742......15790.......330840.........6894210..........143484144

....2644.....101398......3824528.......143484144.........5376199876

....9418.....650928.....44196144......2985166430.......201368802704

...33544....4178316....510685176.....62100488254......7541722428052

..119470...26820102...5900818062...1291848133836....282448223982692

..425500..172154058..68181837738..26873571586520..10578025710796398

.1515442.1105028596.787815537064.559034577488572.396159194076516486

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -9*a(n-2) -9*a(n-3) +10*a(n-4) +3*a(n-5) -2*a(n-6)

k=3: [order 11]

k=4: [order 22]

k=5: [order 46]

k=6: [order 87]

Example

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

Crossrefs

Column 1 is A180143(n+1)

Sequence in context: A187277 A316443 A223313 * A235449 A235736 A235517

Adjacent sequences: A235676 A235677 A235678 * A235680 A235681 A235682

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 13 2014

Status

approved