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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
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved