A250656 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

9, 16, 19, 25, 34, 39, 36, 53, 70, 79, 49, 76, 109, 142, 159, 64, 103, 156, 221, 286, 319, 81, 134, 211, 316, 445, 574, 639, 100, 169, 274, 427, 636, 893, 1150, 1279, 121, 208, 345, 554, 859, 1276, 1789, 2302, 2559, 144, 251, 424, 697, 1114, 1723, 2556, 3581

Offset: 1

Author

R. H. Hardin, Nov 26 2014

Keywords

• nonn
• tabl

Comments

Table starts

....9...16....25....36....49....64....81...100...121...144...169....196....225

...19...34....53....76...103...134...169...208...251...298...349....404....463

...39...70...109...156...211...274...345...424...511...606...709....820....939

...79..142...221...316...427...554...697...856..1031..1222..1429...1652...1891

..159..286...445...636...859..1114..1401..1720..2071..2454..2869...3316...3795

..319..574...893..1276..1723..2234..2809..3448..4151..4918..5749...6644...7603

..639.1150..1789..2556..3451..4474..5625..6904..8311..9846.11509..13300..15219

.1279.2302..3581..5116..6907..8954.11257.13816.16631.19702.23029..26612..30451

.2559.4606..7165.10236.13819.17914.22521.27640.33271.39414.46069..53236..60915

.5119.9214.14333.20476.27643.35834.45049.55288.66551.78838.92149.106484.121843

Examples

			Some solutions for n=4 k=4
..1..1..0..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..0..0
..0..0..0..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
..0..0..0..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..1..1....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..1..1....0..1..1..1..1....1..1..1..1..1....0..0..0..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..880

Crossrefs

Column 1 is A052549(n+1)

Column 2 is A176449

Column 3 is A156127(n+1)

Column 4 is A048487(n+2)

Row 1 is A000290(n+2)

Row 2 is A168244(n+3)

Formula

Empirical: T(n,k) = 2^(n-1)*k^2 + (5*2^(n-1)-1)*k + 2^(n+1)

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1) +(5*2^(n-1) -1) +2^(n+1)

k=2: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*4 +(5*2^(n-1) -1)*2 +2^(n+1)

k=3: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*9 +(5*2^(n-1) -1)*3 +2^(n+1)

k=4: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*16 +(5*2^(n-1) -1)*4 +2^(n+1)

k=5: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*25 +(5*2^(n-1) -1)*5 +2^(n+1)

k=6: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*36 +(5*2^(n-1) -1)*6 +2^(n+1)

k=7: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*49 +(5*2^(n-1) -1)*7 +2^(n+1)

Empirical for row n:

n=1: a(n) = 1*n^2 + 4*n + 4

n=2: a(n) = 2*n^2 + 9*n + 8

n=3: a(n) = 4*n^2 + 19*n + 16

n=4: a(n) = 8*n^2 + 39*n + 32

n=5: a(n) = 16*n^2 + 79*n + 64

n=6: a(n) = 32*n^2 + 159*n + 128

n=7: a(n) = 64*n^2 + 319*n + 256