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
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
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.
Comments