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

1,1

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

Links

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

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

Example

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

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)

Sequence in context: A335437 A034040 A048279 * A072836 A373265 A068824

Adjacent sequences: A250653 A250654 A250655 * A250657 A250658 A250659

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2014

Status

approved