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A250755
T(n,k)=Number of (n+1)X(k+1) 0..2 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
15
32, 72, 105, 129, 237, 332, 203, 423, 756, 1029, 294, 663, 1353, 2361, 3152, 402, 957, 2123, 4239, 7272, 9585, 527, 1305, 3066, 6663, 13089, 22197, 29012, 669, 1707, 4182, 9633, 20603, 40023, 67356, 87549, 828, 2163, 5471, 13149, 29814, 63063, 121593
OFFSET
1,1
COMMENTS
Table starts
.....32......72.....129.....203.....294......402......527......669......828
....105.....237.....423.....663.....957.....1305.....1707.....2163.....2673
....332.....756....1353....2123....3066.....4182.....5471.....6933.....8568
...1029....2361....4239....6663....9633....13149....17211....21819....26973
...3152....7272...13089...20603...29814....40722....53327....67629....83628
...9585...22197...40023...63063...91317...124785...163467...207363...256473
..29012...67356..121593..191723..277746...379662...497471...631173...780768
..87549..203601..367839..580263..840873..1149669..1506651..1911819..2365173
.263672..613872.1109649.1751003.2537934..3470442..4548527..5772189..7141428
.793065.1847757.3341223.5273463.7644477.10454265.13702827.17390163.21516273
LINKS
FORMULA
Empirical: T(n,k) = (3*(k+1)*(5*k+4)*3^n - (8*k^2+8*k)*2^n + (5*k^2-7*k))/4
Empirical for column k:
k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (27*3^n-8*2^n-1)/2
k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (63*3^n-24*2^n+3)/2
k=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (114*3^n-48*2^n+12)/2
k=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (180*3^n-80*2^n+26)/2
k=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (261*3^n-120*2^n+45)/2
k=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (357*3^n-168*2^n+69)/2
k=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (468*3^n-224*2^n+98)/2
Empirical for row n:
n=1: a(n) = (17/2)*n^2 + (29/2)*n + 9
n=2: a(n) = 27*n^2 + 51*n + 27
n=3: a(n) = (173/2)*n^2 + (329/2)*n + 81
n=4: a(n) = 273*n^2 + 513*n + 243
n=5: a(n) = (1697/2)*n^2 + (3149/2)*n + 729
n=6: a(n) = 2607*n^2 + 4791*n + 2187
n=7: a(n) = (15893/2)*n^2 + (29009/2)*n + 6561
EXAMPLE
Some solutions for n=4 k=4
..1..1..1..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..1..1..1..2....2..2..2..2..2....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..2....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1
..0..1..1..1..2....1..1..1..2..2....2..2..2..2..2....0..0..2..2..2
..0..1..1..1..2....0..0..0..1..2....0..1..1..1..2....0..0..2..2..2
CROSSREFS
Column 1 is A053152(n+3)
Sequence in context: A228665 A101539 A106700 * A216427 A104026 A216417
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved