A194998 T(n,k)=Number of lower triangles of an n X n 0..k array with each element differing from all of its horizontal and vertical neighbors by one.
2, 3, 2, 4, 6, 2, 5, 10, 20, 2, 6, 14, 42, 80, 2, 7, 18, 66, 248, 576, 2, 8, 22, 90, 458, 2290, 4608, 2, 9, 26, 114, 672, 4990, 31042, 69632, 2, 10, 30, 138, 888, 7858, 81014, 641376, 1114112, 2, 11, 34, 162, 1104, 10804, 138956, 2059822, 19753266, 34603008, 2, 12, 38
Offset: 1
Examples
Some solutions for n=4 k=4 ..3........2........3........0........1........4........4........3 ..2.3......1.0......2.1......1.0......2.1......3.2......3.2......2.1 ..1.2.1....0.1.2....3.2.3....2.1.2....1.0.1....2.1.2....4.3.2....1.2.3 ..0.1.0.1..1.2.1.0..2.3.2.3..1.0.1.2..2.1.2.1..1.2.1.0..3.2.3.4..2.1.2.1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..373
Formula
Empirical for rows:
T(1,k) = 1*k + 1
T(2,k) = 4*k - 2
T(3,k) = 24*k - 30 for k>2
T(4,k) = 216*k - 408 for k>4
T(5,k) = 2952*k - 6910 for k>6
T(6,k) = 61488*k - 169100 for k>8
T(7,k) = 1957392*k - 6016308 for k>10
Generalizing, T(n,k) = A145237(n)*k + const(n), for k>2*n-4
Comments