A266033 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than itself.

1, 3, 1, 5, 11, 1, 11, 50, 55, 1, 26, 315, 481, 263, 1, 55, 2142, 5594, 4659, 1248, 1, 119, 13796, 121029, 118489, 45361, 5959, 1, 263, 89487, 2045306, 8260441, 2482216, 440405, 28399, 1, 573, 578659, 33026298, 408513208, 576560236, 52086421, 4281953

Offset

1,2

Comments

Table starts

.1.......3..........5.............11.................26......................55

.1......11.........50............315...............2142...................13796

.1......55........481...........5594.............121029.................2045306

.1.....263.......4659.........118489............8260441...............408513208

.1....1248......45361........2482216..........576560236.............82171346791

.1....5959.....440405.......52086421........40462691139..........16683384355551

.1...28399....4281953.....1092258910......2834665076351........3378465528248312

.1..135383...41605113....22909266015....198722506983924......684927787385220826

.1..645407..404371841...480473869537..13929598180007373...138808963888717658013

.1.3076736.3929676961.10077157027608.976418236686388550.28134602812633017755802

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 3*a(n-1) +7*a(n-2) +7*a(n-3) -a(n-4)

k=3: a(n) = 5*a(n-1) +46*a(n-2) +6*a(n-3) -72*a(n-4)

k=4: [order 16] for n>17

k=5: [order 38] for n>41

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)

n=2: [order 26]

Example

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

Crossrefs

Row 1 is A196423.

Sequence in context: A324017 A063853 A219078 * A105064 A073496 A176122

Adjacent sequences: A266030 A266031 A266032 * A266034 A266035 A266036

Keyword

nonn,tabl

Author

_R. H. Hardin_, Dec 20 2015

Status

approved