A234393 T(n,k) = number of (n+2) X (k+2) 0..3 arrays with no increasing sequence of length 3 vertically, diagonally downwards or antidiagonally downwards.

196316, 10683130, 9292808, 585790562, 1687142836, 426876528, 32129615500, 312048302829, 252617381130, 19562241288, 1761338821822, 57796098504371, 153633836957604, 37540308719262, 893326493316, 96553476935058

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

Empirical for column k:

k=1: [linear recurrence of order 44]

Empirical for row n:

n=1: [linear recurrence of order 20]

n=2: [order 85]

Example

Table starts:
        196316         10683130            585790562              32129615500
       9292808       1687142836         312048302829           57796098504371
     426876528     252617381130      153633836957604        93663449566825996
   19562241288   37540308719262    74663552616253924    148995535070508548075
  893326493316 5540782611170014 35875918677964045614 233248382982183041074476
  ...
Some solutions for n=1 k=4
..0..0..0..1..1..3....0..0..0..0..3..0....0..0..0..1..2..0....0..0..0..1..3..1
..0..0..0..1..0..0....0..0..0..1..0..0....0..0..0..1..0..3....0..0..0..0..1..1
..0..0..0..2..1..0....0..0..0..0..1..2....0..0..0..0..1..1....0..0..0..2..3..1

Crossrefs

Columns 1..4 are A234389, A234390, A234391, A234392.

Rows 1..4 are A234394, A234395, A234396, A234397.

Cf. A234380.

Sequence in context: A074388 A234996 A234389 * A234394 A202434 A179253

Adjacent sequences: A234390 A234391 A234392 * A234394 A234395 A234396

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2013

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

Status

approved