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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A192760(n+2)

Sequence in context: A342409 A329007 A368120 * A251292 A177458 A228009

Adjacent sequences: A250726 A250727 A250728 * A250730 A250731 A250732

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2014

Status

approved