A250691 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

104, 543, 520, 2541, 2920, 2512, 11150, 13906, 15246, 11736, 47002, 60508, 74631, 76320, 53032, 193117, 249512, 324648, 383440, 362241, 233300, 780551, 995624, 1315446, 1670016, 1848953, 1647460, 1005121, 3122604, 3894542, 5098590, 6671458

Offset

1,1

Comments

Table starts

......104.......543.......2541.......11150.......47002......193117......780551

......520......2920......13906.......60508......249512......995624.....3894542

.....2512.....15246......74631......324648.....1315446.....5098590....19218493

....11736.....76320.....383440.....1670016.....6671458....25235016....92169818

....53032....362241....1848953.....8038566....31728758...117793753...420283865

...233300...1647460....8474002....36673634...143136866...523260542..1832718604

..1005121...7249825...37322413...160222342...617657415..2224688673..7662909389

..4260728..31113316..159438246...676640344..2571646112..9121206688.30911828018

.17835379.131014715..665575403..2784280670.10412478449.36332194553

.73930174.543845812.2731006288.11235235268.41269021168

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: [linear recurrence of order 7] for n>11

k=2: [order 13] for n>17

k=3: [same order 13] for n>17

k=4: [same order 13] for n>17

k=5: [same order 13] for n>17

k=6: [same order 13] for n>17

k=7: [same order 13] for n>17

Empirical for row n:

n=1: [linear recurrence of order 7, cf. A250692]

n=2: [order 10, cf. A250693]

n=3: [order 16, cf. A250694]

n=4: [same order 16, cf. A250695]

n=5: [same order 16, cf. A250696]

n=6: [same order 16, cf. A250697]

n=7: [same order 16, cf. A250698].

Example

Some solutions for n=3 k=4
..2..3..1..0..0....2..2..3..2..2....2..2..1..1..0....0..1..0..0..0
..2..3..2..1..1....0..0..1..0..0....2..2..2..2..3....0..1..0..0..1
..1..2..1..0..0....0..0..1..1..1....1..1..1..1..2....1..2..1..1..2
..0..1..2..1..3....0..0..1..1..2....0..0..0..0..3....1..2..1..1..2

Crossrefs

Column 1 is A250669.

Rows 1-7 are A250692, ..., A250698.

Sequence in context: A234201 A383390 A250669 * A250692 A250676 A250677

Adjacent sequences: A250688 A250689 A250690 * A250692 A250693 A250694

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2014

Status

approved