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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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Sep 07 2011
STATUS
approved