A266012 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 4, 6, 1, 1, 2, 4, 4, 14, 1, 1, 1, 1, 11, 9, 22, 2, 1, 1, 4, 18, 27, 14, 46, 1, 1, 2, 4, 27, 61, 70, 21, 102, 1, 1, 1, 1, 43, 75, 154, 182, 44, 190, 2, 1, 1, 4, 62, 281, 486, 473, 483, 52, 374, 1, 1, 2, 4, 112, 697, 1602, 2208, 1561, 1281, 129, 782, 1, 1, 1, 1

Offset

1,4

Comments

Table starts

.1.1...2...1....1.....2.......1........1........2........1..........1

.1.1...2...4....4.....1.......4........4........1........4..........4

.1.2...6...4...11....18......27.......43.......62......112........191

.1.1..14...9...27....61......75......281......697.....1182.......3379

.1.1..22..14...70...154.....486.....1602.....5777....10188......28506

.1.2..46..21..182...473....2208....10811....27582....48585.....208339

.1.1.102..44..483..1561...10708....62684...145344...253394....1663567

.1.1.190..52.1281..4909...53384...348557...850986..1738887...15011717

.1.2.374.129.3389.15560..255936..2118339..4845667.10779958..123629847

.1.1.782.138.8986.49716.1264666.12427613.27769481.64933909.1062244523

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

k=2: a(n) = a(n-3)

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

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

k=5: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) +2*a(n-4) -3*a(n-5) -a(n-6) for n>12

k=6: [order 19] for n>21

k=7: [order 24] for n>28

Empirical for row n:

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

n=2: a(n) = a(n-3) for n>6

n=3: [order 15] for n>19

n=4: [order 44] for n>53

Example

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

Crossrefs

Row 2 is A173259(n+6).

Sequence in context: A070242 A242748 A374163 * A202111 A187759 A358565

Adjacent sequences: A266009 A266010 A266011 * A266013 A266014 A266015

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2015

Status

approved