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

1,7

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000217(n-2)

Column 2 is A102083(n-3)

Sequence in context: A114588 A253223 A121745 * A089312 A246674 A363340

Adjacent sequences: A252980 A252981 A252982 * A252984 A252985 A252986

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2014

Status

approved