|
| |
|
|
A195248
|
|
T(n,k) = Number of lower triangles of an n X n 0..k array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.
|
|
11
|
|
|
|
2, 3, 8, 4, 27, 64, 5, 46, 729, 1024, 6, 65, 1682, 59049, 32768, 7, 84, 2729, 190514, 14348907, 2097152, 8, 103, 3776, 357847, 67379894, 10460353203, 268435456, 9, 122, 4823, 533142, 147824001, 74236765958, 22876792454961, 68719476736, 10, 141
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Table starts
.......2...........3...........4............5............6............7
.......8..........27..........46...........65...........84..........103
......64.........729........1682.........2729.........3776.........4823
....1024.......59049......190514.......357847.......533142.......709613
...32768....14348907....67379894....147824001....237368212....329060365
.2097152.10460353203.74236765958.192172956591.333437946202.481573562101
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for rows:
T(1,k) = 1*k + 1,
T(2,k) = 19*k - 11
T(3,k) = 1047*k - 1459 for k>2,
T(4,k) = 176471*k - 349213 for k>4,
T(5,k) = 92031109*k - 223153377 for k>6,
T(6,k) = 149824887097*k - 417651128341 for k>8,
T(7,k) = 764465228592699*k - 2364216638005277 for k>10,
Generalizing, T(n,k) = A195214(n)*k + const(n) for k>2*n-4.
|
|
|
EXAMPLE
|
Some solutions for n=6, k=5
..4............1............5............0............0............1
..5.3..........1.3..........5.4..........1.2..........0.2..........0.0
..5.4.5........1.2.4........3.4.4........1.3.1........1.0.0........2.1.2
..4.3.4.4......3.3.3.3......5.3.5.4......2.1.1.2......0.1.1.0......0.0.2.2
..5.4.2.2.4....4.5.4.5.5....4.3.5.4.3....2.3.1.3.1....2.0.2.2.0....2.0.1.2.4
..4.3.2.2.4.4..3.5.3.3.5.5..3.5.5.3.3.1..4.2.2.1.1.0..0.2.0.2.0.1..1.1.0.2.4.4
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
