A224173 T(n,k) = number of n X k 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

4, 16, 10, 50, 100, 20, 130, 684, 400, 35, 296, 3526, 4739, 1225, 56, 610, 14751, 38561, 22988, 3136, 84, 1163, 52591, 242114, 272130, 87878, 7056, 120, 2083, 165212, 1253770, 2335459, 1460836, 282372, 14400, 165, 3544, 468292, 5588411, 15925611

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..178

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,3,6,9,12.

Empirical: rows n=1..5 are polynomials of degree 6*n for k>0,0,0,2,6.

Example

Table starts:
    4    16       50       130         296          610           1163
   10   100      684      3526       14751        52591         165212
   20   400     4739     38561      242114      1253770        5588411
   35  1225    22988    272130     2335459     15925611       91494280
   56  3136    87878   1460836    16625026    143558572     1012166273
   84  7056   282372   6425876    95808564   1038484760     8857798353
  120 14400   794220  24197608   468021427   6360047093    65713691148
  165 27225  2010035  80350989  1994287334  33901838632   426013124302
  220 48400  4668304 240416852  7568051210 160168789130  2451904991177
  286 81796 10095924 658890738 25994968917 680269560125 12667946702827
  ...
Some solutions for n=3 k=4
..0..0..1..0....0..0..1..2....0..0..3..0....0..2..0..0....0..3..3..1
..1..3..3..1....0..1..3..2....3..3..3..1....1..2..0..0....1..3..3..1
..1..3..3..3....0..3..3..2....3..3..3..2....2..2..1..0....1..3..3..3

Crossrefs

Main diagonal is A224167.

Columns 1..7 are A000292(n+1), A001249, A224168, A224169, A224170, A224171, A224172.

Rows 1..7 are A223659, A223865, A224174, A224175, A224176, A224177, A224178.

Cf. A223838.

Sequence in context: A067178 A346460 A181717 * A223864 A223987 A224123

Adjacent sequences: A224170 A224171 A224172 * A224174 A224175 A224176

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 31 2013

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

Status

approved