A250729 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, 22, 18, 50, 46, 33, 114, 110, 85, 58, 257, 257, 208, 144, 99, 579, 596, 496, 365, 230, 166, 1302, 1376, 1158, 885, 600, 350, 275, 2927, 3173, 2699, 2092, 1500, 942, 513, 452, 6578, 7310, 6257, 4889, 3605, 2434, 1418, 728, 739, 14782, 16838, 14520, 11377, 8514

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn
• tabl

Comments

Table starts

....9...22...50...114...257...579...1302...2927....6578...14782...33216

...18...46..110...257...596..1376...3173...7310...16838...38777...89300

...33...85..208...496..1158..2699...6257..14520...33640...77999..180744

...58..144..365...885..2092..4889..11377..26419...61330..142336..330417

...99..230..600..1500..3605..8514..19887..46315..107565..249853..579962

..166..350..942..2434..6016.14437..34069..79704..185684..431691.1002869

..275..513.1418..3807..9728.23941..57397.135645..317769..741367.1725118

..452..728.2065..5760.15297.38821..95231.228455..540546.1268605.2963321

..739.1006.2918..8465.23407.61554.155263.380220..912438.2161980.5081193

.1204.1358.4022.12119.34943.95438.248537.623913.1525255.3661515.8684030

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1860

Crossrefs

Column 1 is A192760(n+2)

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)

k=2: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6); also a polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2

k=3: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6); also a polynomial of degree 4 plus a quasipolynomial of degree 0 with period 2

k=4: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7) for n>8; also a polynomial of degree 5 plus a quasipolynomial of degree 0 with period 2 for n>1

k=5: [order 8; also a polynomial of degree 6 plus a quasipolynomial of degree 0 with period 2] for n>10

k=6: [order 9; also a polynomial of degree 7 plus a quasipolynomial of degree 0 with period 2] for n>14

k=7: [order 10; also a polynomial of degree 8 plus a quasipolynomial of degree 0 with period 2] for n>17

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3) +a(n-4)

n=2: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) for n>4

n=3: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-3) +12*a(n-4) -2*a(n-5) -3*a(n-6) +a(n-7) for n>8

n=4: [order 7] for n>9

n=5: [order 9] for n>12

n=6: [order 11] for n>15

n=7: [order 14] for n>19