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

1,1

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

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

Example

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

Crossrefs

Sequence in context: A043263 A321326 A118978 * A215190 A214943 A202864

Adjacent sequences: A194995 A194996 A194997 * A194999 A195000 A195001

Keyword

nonn,tabl

Author

R. H. Hardin Sep 07 2011

Status

approved