A224262 T(n,k) = number of n X k 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
3, 9, 6, 22, 36, 10, 46, 158, 100, 15, 86, 548, 648, 225, 21, 148, 1600, 3096, 2017, 441, 28, 239, 4102, 12032, 12467, 5246, 784, 36, 367, 9503, 40182, 59855, 41012, 11990, 1296, 45, 541, 20299, 119367, 240829, 238366, 116692, 24842, 2025, 55, 771, 40570
Offset: 1
Examples
Table starts: 3 9 22 46 86 148 239 367 541 6 36 158 548 1600 4102 9503 20299 40570 10 100 648 3096 12032 40182 119367 322885 808618 15 225 2017 12467 59855 240829 850875 2717731 8000608 21 441 5246 41012 238366 1122522 4542734 16423026 54399996 28 784 11990 116692 816361 4480391 20568693 82733667 301228048 36 1296 24842 296646 2485967 15921905 83124099 371699763 1478187738 45 2025 47643 688533 6868203 51343083 306179180 1530419762 6671184875 55 3025 85838 1482310 17467782 152072846 1038489172 5835731860 28072690614 66 4356 146878 2995516 41364960 417672794 3266157979 20709405119 110622071553 ... Some solutions for n=3 k=4: ..1..1..0..0....1..1..1..1....1..1..2..1....0..2..1..0....0..0..0..0 ..2..1..1..0....1..2..2..1....2..2..2..1....0..2..1..1....0..0..2..0 ..2..2..1..1....2..2..2..1....2..2..2..2....0..2..2..1....0..0..2..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..241
Crossrefs
Formula
Empirical: columns k=1..7 are polynomials of order 2*k for n>0,0,0,2,4,6,8.
Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,0,2,4,6,8.
Extensions
Name corrected by Andrew Howroyd, Mar 18 2025