A251088 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements

27, 83, 83, 192, 284, 192, 420, 616, 616, 420, 872, 1306, 1165, 1306, 872, 1782, 2534, 2362, 2362, 2534, 1782, 3593, 4848, 4379, 4718, 4379, 4848, 3593, 7215, 9086, 8284, 8512, 8512, 8284, 9086, 7215, 14443, 17102, 15411, 15780, 14891, 15780, 15411

Offset

1,1

Comments

Table starts

....27....83....192....420....872...1782...3593....7215...14443...28891...57762

....83...284....616...1306...2534...4848...9086...17102...32336...61836..119420

...192...616...1165...2362...4379...8284..15411...29142...55429..106880..207889

...420..1306...2362...4718...8512..15780..28616...52934...98550..186788..358250

...872..2534...4379...8512..14891..27040..48017...87488..160737..301824..574763

..1782..4848...8284..15780..27040..47932..82898..147152..263698..484744..907152

..3593..9086..15411..28616..48017..82898.139553..240972..420611..755534.1387095

..7215.17102..29142..52934..87488.147152.240972..402854..680446.1184344.2115062

.14443.32336..55429..98550.160737.263698.420611..680446.1109887.1863898.3220133

.28891.61836.106880.186788.301824.484744.755534.1184344.1863898.3007772.4993492

Links

R. H. Hardin, Table of n, a(n) for n = 1..544

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -8*a(n-2) +2*a(n-3) +7*a(n-4) -7*a(n-5) +2*a(n-6) for n>7

k=2: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

k=3: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

k=4: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

k=5: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

k=6: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

k=7: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8

Example

Some solutions for n=4 k=4
..0..0..1..1..2....0..1..1..1..2....0..1..2..2..2....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....2..2..2..2..2
..1..1..1..1..1....0..0..0..0..1....2..2..2..2..2....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....1..1..1..1..1
..1..1..1..0..0....2..1..0..0..0....2..2..2..1..1....0..0..0..0..0

Crossrefs

Sequence in context: A042434 A042436 A042438 * A044981 A251081 A161340

Adjacent sequences: A251085 A251086 A251087 * A251089 A251090 A251091

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved