A253524 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically

81, 470, 470, 2180, 2724, 2180, 9623, 10706, 10706, 9623, 42669, 42476, 30013, 42476, 42669, 192393, 169828, 84684, 84684, 169828, 192393, 876277, 666239, 256914, 162815, 256914, 666239, 876277, 4010555, 2544290, 791232, 370028, 370028, 791232

Offset

1,1

Comments

Table starts

.......81.......470.....2180.....9623....42669...192393....876277...4010555

......470......2724....10706....42476...169828...666239...2544290...9487609

.....2180.....10706....30013....84684...256914...791232...2419612...7338525

.....9623.....42476....84684...162815...370028...930046...2475610...6886675

....42669....169828...256914...370028...673229..1439791...3429207...8936967

...192393....666239...791232...930046..1439791..2662626...5591131..13347833

...876277...2544290..2419612..2475610..3429207..5591131..10168992..21354009

..4010555...9487609..7338525..6886675..8936967.13347833..21354009..38531995

.18395493..34708223.22126888.19760474.24799705.35219532..51569897..81282413

.84458827.125073383.66487395.57829329.71469938.98975447.137921376.198445532

Links

R. H. Hardin, Table of n, a(n) for n = 1..238

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -15*a(n-2) -12*a(n-3) +44*a(n-4) -8*a(n-5) -16*a(n-6) for n>13

k=2: [order 9] for n>17

k=3: [order 8] for n>16

k=4: [order 8] for n>16

k=5: [order 7] for n>15

k=6: [same order 7] for n>15

k=7: [same order 7] for n>15

Example

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

Crossrefs

Sequence in context: A236354 A236349 A334036 * A254422 A253517 A237683

Adjacent sequences: A253521 A253522 A253523 * A253525 A253526 A253527

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2015

Status

approved