A266101 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors exactly one smaller than itself.

1, 3, 1, 4, 5, 1, 5, 13, 16, 1, 9, 36, 64, 39, 1, 16, 100, 161, 230, 105, 1, 25, 233, 736, 929, 1012, 272, 1, 39, 680, 3846, 6307, 4893, 3928, 715, 1, 64, 2201, 16103, 52171, 53442, 26948, 16428, 1869, 1, 105, 6508, 62778, 371130, 841668, 457738, 145274, 65736

Offset

1,2

Comments

Table starts

.1.....3.......4........5..........9...........16.............25

.1.....5......13.......36........100..........233............680

.1....16......64......161........736.........3846..........16103

.1....39.....230......929.......6307........52171.........371130

.1...105....1012.....4893......53442.......841668........9880139

.1...272....3928....26948.....457738.....12401485......240721036

.1...715...16428...145274....3899732....192212829.....6206090116

.1..1869...65736...790986...33335734...2895851074...154469020054

.1..4896..269908..4286644..284461696..44366390231..3932140956510

.1.12815.1091720.23281595.2429715557.672954998752.98694163378141

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +12*a(n-2) +5*a(n-3) -12*a(n-4) -2*a(n-5)

k=4: [order 15] for n>16

k=5: [order 17] for n>20

k=6: [order 72] for n>75

Empirical for row n:

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

n=2: [order 16] for n>19

n=3: [order 64] for n>68

Example

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

Crossrefs

Column 2 is A121646(n+2).

Row 1 is A195971.

Sequence in context: A366977 A029637 A097207 * A118469 A319649 A198553

Adjacent sequences: A266098 A266099 A266100 * A266102 A266103 A266104

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2015

Status

approved