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.

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

Author

R. H. Hardin, Sep 13 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..132

Crossrefs

Column 1 is A006125(n+1).

Column 2 is A047656(n+1).

Cf. A195214.

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.