A234380 T(n,k) = number of (n+2) X (k+2) 0..2 arrays with no increasing sequence of length 3 vertically, diagonally downwards or antidiagonally downwards.

16584, 406416, 372690, 9995040, 24485940, 8280018, 245837376, 1622352843, 1443868938, 183669567, 6045322368, 107611542837, 254778511950, 84764693441, 4070647527, 148657436928, 7134211462374, 45066201971526, 39700991817357

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: [linear recurrence of order 19]

k=2: [order 55]

Empirical for row n:

n=1: a(n) = 24*a(n-1) -12*a(n-2) +624*a(n-3) +1056*a(n-4) -8448*a(n-5) -9216*a(n-6)

n=2: [order 23]

n=3: [order 58]

Example

Table starts:
        16584          406416            9995040              245837376
       372690        24485940         1622352843           107611542837
      8280018      1443868938       254778511950         45066201971526
    183669567     84764693441     39700991817357      18662305835280147
   4070647527   4966249171199   6163727050266589    7686715868506969433
  90202925160 290807719744802 955881551862891819 3160465819880176888222
  ...
Some solutions for n=1 k=4:
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..1..0..0..0..0..0....0..2..0..0..2..0....0..0..0..1..1..0....1..2..2..0..2..2
..1..2..1..2..1..2....1..1..2..0..2..1....1..0..0..0..0..1....0..1..2..2..0..2

Crossrefs

Columns 1..6 are A234374, A234375, A234376, A234377, A234378, A234379.

Rows 1..6 are A234381, A234382, A234383, A234384, A234385, A234386.

Cf. A234393.

Sequence in context: A344241 A344242 A234374 * A234381 A236638 A250930

Adjacent sequences: A234377 A234378 A234379 * A234381 A234382 A234383

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2013

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

Status

approved