A237859 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors

2, 4, 4, 7, 14, 7, 12, 41, 41, 12, 21, 114, 184, 114, 21, 37, 325, 773, 773, 325, 37, 65, 943, 3373, 4826, 3373, 943, 65, 114, 2731, 15038, 31651, 31651, 15038, 2731, 114, 200, 7876, 66838, 213165, 315896, 213165, 66838, 7876, 200, 351, 22702, 295601, 1428967

Offset

1,1

Comments

Table starts

...2.....4.......7........12..........21............37..............65

...4....14......41.......114.........325...........943............2731

...7....41.....184.......773........3373.........15038...........66838

..12...114.....773......4826.......31651........213165.........1428967

..21...325....3373.....31651......315896.......3255233........33328972

..37...943...15038....213165.....3255233......51576880.......810629762

..65..2731...66838...1428967....33328972.....810629762.....19525964230

.114..7876..295601...9520138...338653847...12628484789....465620654717

.200.22702.1306735..63406826..3440498469..196722783963..11103987320260

.351.65489.5781785.422805151.35005538562.3069861742669.265336172863532

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 21]

k=5: [order 46]

k=6: [order 98]

Example

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

Crossrefs

Column 1 is A005251(n+3)

Sequence in context: A227751 A268995 A205744 * A240338 A227103 A223644

Adjacent sequences: A237856 A237857 A237858 * A237860 A237861 A237862

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 14 2014

Status

approved