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.

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

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A053152(n+3)

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