login
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.
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 21 2015
STATUS
approved