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

Author

R. H. Hardin, Dec 21 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A121646(n+2).

Row 1 is A195971.

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