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

Author

R. H. Hardin Sep 07 2011

Keywords

• nonn
• tabl

Comments

Table starts

.2.......3........4........5.........6.........7.........8.........9........10

.2.......6.......10.......14........18........22........26........30........34

.2......20.......42.......66........90.......114.......138.......162.......186

.2......80......248......458.......672.......888......1104......1320......1536

.2.....576.....2290.....4990......7858.....10804.....13754.....16706.....19658

.2....4608....31042....81014....138956....199988....261324....322806....384292

.2...69632...641376..2059822...3816148...5740166...7686580...9643120..11600228

.2.1114112.19753266.78060014.159427052.251606900.346018484.441301618.536657628

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