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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
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
Column 1 is A006125(n+1).
Column 2 is A047656(n+1).
Cf. A195214.
Sequence in context: A195232 A093898 A194931 * A229870 A202651 A334859
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 13 2011
STATUS
approved