A229428 T(n,k) = Number of n X k 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
3, 5, 5, 8, 12, 8, 12, 27, 27, 12, 17, 55, 83, 55, 17, 23, 102, 222, 222, 102, 23, 30, 175, 524, 754, 524, 175, 30, 38, 282, 1116, 2204, 2204, 1116, 282, 38, 47, 432, 2187, 5700, 7816, 5700, 2187, 432, 47, 57, 635, 4005, 13345, 24126, 24126, 13345, 4005, 635, 57
Offset: 1
Examples
Some solutions for n=4 k=4 ..2..2..1..0....1..1..0..0....1..1..0..0....2..1..1..1....1..0..0..0 ..2..2..1..1....2..1..0..0....2..1..0..0....2..1..1..1....1..1..1..1 ..2..2..1..1....2..1..1..1....2..1..1..1....2..2..2..1....2..2..1..1 ..2..2..2..1....2..1..1..1....2..2..1..1....2..2..2..2....2..2..2..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..480
Formula
Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 2
k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2, A229422
k=3: [polynomial of degree 6], A229423
k=4: [polynomial of degree 8], A229424
k=5: [polynomial of degree 10], A229425
k=6: [polynomial of degree 12], A229426
k=7: [polynomial of degree 14]
Comments