A251192 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column

512, 1728, 1728, 5832, 7776, 5832, 19683, 34992, 34992, 19683, 46656, 157464, 209952, 157464, 46656, 110592, 466560, 1259712, 1259712, 466560, 110592, 262144, 1382400, 4665600, 10077696, 4665600, 1382400, 262144, 512000, 4096000, 17280000

Offset

1,1

Comments

Table starts

.....512.....1728.......5832.......19683........46656........110592

....1728.....7776......34992......157464.......466560.......1382400

....5832....34992.....209952.....1259712......4665600......17280000

...19683...157464....1259712....10077696.....46656000.....216000000

...46656...466560....4665600....46656000....259200000....1440000000

..110592..1382400...17280000...216000000...1440000000....9600000000

..262144..4096000...64000000..1000000000...8000000000...64000000000

..512000..9600000..180000000..3375000000..31500000000..294000000000

.1000000.22500000..506250000.11390625000.124031250000.1350562500000

.1953125.52734375.1423828125.38443359375.488373046875.6204146484375

Links

R. H. Hardin, Table of n, a(n) for n = 1..794

Formula

Empirical for column k:

k=1: [linear recurrence of order 26; also a polynomial of degree 9 plus a quasipolynomial of degree 7 with period 3]

k=2: [order 35; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 3]

k=3: [order 44; also a polynomial of degree 15 plus a quasipolynomial of degree 13 with period 3]

k=4: [order 53; also a polynomial of degree 18 plus a quasipolynomial of degree 16 with period 3]

k=5: [order 62; also a polynomial of degree 21 plus a quasipolynomial of degree 19 with period 3]

Example

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

Crossrefs

Column 4 is A250594

Column 7 is A250861

Sequence in context: A195092 A235192 A203451 * A251187 A223333 A135273

Adjacent sequences: A251189 A251190 A251191 * A251193 A251194 A251195

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved