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: A234208 A234201 A250669 * A250692 A250676 A250677

Adjacent sequences: A250688 A250689 A250690 * A250692 A250693 A250694

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2014

Status

approved