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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
15
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
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: A373747 A329007 A368120 * A251292 A177458 A228009
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved