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A253749
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
15
81, 450, 450, 1998, 2723, 1998, 7803, 10182, 16625, 7803, 28107, 29737, 77414, 75959, 28107, 95940, 70590, 247252, 382973, 305707, 95940, 315576, 148134, 583698, 1143174, 1636717, 1087364, 315576, 1011357, 298760, 1204422, 2351928, 5195288
OFFSET
1,1
COMMENTS
Table starts
......81......450......1998......7803......28107......95940.....315576
.....450.....2723.....10182.....29737......70590.....148134.....298760
....1998....16625.....77414....247252.....583698....1204422....2363797
....7803....75959....382973...1143174....2351928....4249381....7348144
...28107...305707...1636717...5195288...10966149...19685575...33767784
...95940..1087364...5648005..17656505...36766701...64166071..106040628
..315576..3598487..17980643..54890203..112645903..199063466..333213583
.1011357.11219006..52078415.150904540..295452432..515093745..871426149
.3181653.33417573.140931619.390365827..734787935.1244615026.2111246736
.9876870.95950526.357840627.928677156.1658583509.2727201405.4561812863
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
k=2: [order 42] for n>46
k=3: [order 35] for n>45
k=4: [order 35] for n>47
k=5: [order 26] for n>41
k=6: [same order 26] for n>40
k=7: [same order 26] for n>41
Empirical for row n:
n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
n=2: [order 19] for n>25
n=3: [order 23] for n>30
n=4: [order 19] for n>27
n=5: [same order 19] for n>28
n=6: [same order 19] for n>29
n=7: [same order 19] for n>30
Empirical quasipolynomials for column k:
k=5: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
k=6: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>14
k=7: polynomial of degree 10 plus a quasipolynomial of degree 4 with period 4 for n>15
Empirical quasipolynomials for row n:
n=4: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>8
n=5: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>9
n=6: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>10
n=7: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 4 for n>11
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..0..1....0..0..0..0..1....0..1..1..1..2....0..0..0..1..1
..2..1..0..0..0....2..1..0..0..1....1..0..0..0..1....1..0..0..0..0
..2..1..0..0..1....2..1..1..0..1....2..2..2..2..2....2..2..2..2..2
..2..1..0..0..1....2..2..1..1..1....2..1..1..0..2....1..1..1..1..2
CROSSREFS
Sequence in context: A230064 A236710 A236705 * A253375 A204230 A235441
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 11 2015
STATUS
approved