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A250877
T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction
16
90, 288, 440, 678, 1456, 2002, 1328, 3442, 6812, 8736, 2306, 6728, 16262, 30360, 37130, 3680, 11644, 31928, 73122, 131068, 155080, 5518, 18520, 55386, 144248, 317878, 553736, 640002, 7888, 27686, 88212, 250964, 629528, 1350002, 2304492
OFFSET
1,1
COMMENTS
Table starts
.......90.......288.......678......1328.......2306.......3680.......5518
......440......1456......3442......6728......11644......18520......27686
.....2002......6812.....16262.....31928......55386......88212.....131982
.....8736.....30360.....73122....144248.....250964.....400496.....600070
....37130....131068....317878....629528....1097986....1755220....2633198
...155080....553736...1350002...2681528....4685964....7500960...11264166
...640002...2304492...5640102..11227928...19649066...31484612...47315662
..2619056...9488920..23289922..46440248...81358084..130461616..196169030
.10653370..38773148..95366678.190392728..333810066..535577460..805653678
.43144920.157554216.388124562.775558328.1360557884.2183825600.3286063846
LINKS
FORMULA
Empirical: T(n,k) = (((62/3)*k^3+52*k^2+(130/3)*k+12)*4^n -((45/2)*k^3+(81/2)*k^2+18*k)*3^n +(9*k^3-9*k)*2^n +((5/6)*k^3-(5/2)*k^2+(8/3)*k))/3
Empirical for column k:
k=1: a(n) = 8*a(n-1) -19*a(n-2) +12*a(n-3); a(n) = (128*4^n-81*3^n+1)/3
k=2: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (472*4^n-378*3^n+54*2^n+2)/3
k=3: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (1168*4^n-1026*3^n+216*2^n+8)/3
k=4: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (2340*4^n-2160*3^n+540*2^n+24)/3
k=5: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (4112*4^n-3915*3^n+1080*2^n+55)/3
k=6: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (6608*4^n-6426*3^n+1890*2^n+106)/3
k=7: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (9952*4^n-9828*3^n+3024*2^n+182)/3
Empirical for row n:
n=1: a(n) = (34/3)*n^3 + 28*n^2 + (104/3)*n + 16
n=2: a(n) = 55*n^3 + 155*n^2 + 166*n + 64
n=3: a(n) = (788/3)*n^3 + 744*n^2 + (2218/3)*n + 256
n=4: a(n) = (3613/3)*n^3 + 3343*n^2 + (9494/3)*n + 1024
n=5: a(n) = 5328*n^3 + 14468*n^2 + 13238*n + 4096
n=6: a(n) = (68825/3)*n^3 + 61155*n^2 + (163798/3)*n + 16384
n=7: a(n) = (290548/3)*n^3 + 254464*n^2 + (669458/3)*n + 65536
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....1..1..1..1..1
..2..2..2..2..3....2..2..2..3..3....2..2..3..3..3....0..0..0..0..0
..2..2..2..2..3....1..1..2..3..3....1..1..2..3..3....2..2..2..2..2
..0..1..1..1..2....0..0..1..2..2....1..1..2..3..3....0..2..2..2..2
..0..1..1..1..3....0..0..2..3..3....0..0..1..3..3....0..2..2..3..3
CROSSREFS
Sequence in context: A237131 A363729 A255784 * A250878 A027621 A331259
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 28 2014
STATUS
approved