A252983 T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

0, 0, 0, 1, 0, 1, 3, 1, 1, 3, 6, 13, 1, 13, 6, 10, 41, 33, 33, 41, 10, 15, 85, 266, 68, 266, 85, 15, 21, 145, 851, 1247, 1247, 851, 145, 21, 28, 221, 1836, 8487, 4657, 8487, 1836, 221, 28, 36, 313, 3221, 27905, 67537, 67537, 27905, 3221, 313, 36, 45, 421, 5006, 62977

Offset: 1

Author

R. H. Hardin, Dec 25 2014

Keywords

• nonn
• tabl

Comments

Table starts

..0...0....1......3.......6........10..........15............21.............28

..0...0....1.....13......41........85.........145...........221............313

..1...1....1.....33.....266.......851........1836..........3221...........5006

..3..13...33.....68....1247......8487.......27905.........62977.........114433

..6..41..266...1247....4657.....67537......433401.......1481460........3510600

.10..85..851...8487...67537....432842.....5672484......36112108......129234988

.15.145.1836..27905..433401...5672484....60650883.....766674140.....4970634131

.21.221.3221..62977.1481460..36112108...766674140...13458882036...170090480091

.28.313.5006.114433.3510600.129234988..4970634131..170090480091..4857082197177

.36.421.7191.182273.6637020.322183180.18692194423.1139074556531.62656851440792

Examples

			Some solutions for n=4 k=4
..0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..0....0..0..1..1
..0..1..1..1....0..0..0..0....0..0..0..1....0..0..0..1....0..1..1..1
..0..1..1..1....0..0..1..1....0..0..0..1....0..0..1..1....1..1..1..1
..0..1..1..1....0..1..1..1....0..0..1..1....0..0..1..1....1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..480

Crossrefs

Column 1 is A000217(n-2)

Column 2 is A102083(n-3)

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 - (3/2)*n + 1

k=2: a(n) = 8*n^2 - 44*n + 61 for n>2

k=3: a(n) = 200*n^2 - 1615*n + 3341 for n>4

k=4: a(n) = 8192*n^2 - 87808*n + 241153 for n>6

k=5: a(n) = 557568*n^2 - 7467372*n + 25553940 for n>8

k=6: a(n) = 63438848*n^2 - 1019729920*n + 4176308004 for n>10

k=7: a(n) = 12103190528*n^2 - 226960984822*n + 1081747760523 for n>12