A250443 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column

81, 324, 324, 1296, 2160, 1296, 3600, 14400, 14400, 3600, 10000, 60000, 160000, 60000, 10000, 22500, 250000, 1000000, 1000000, 250000, 22500, 50625, 787500, 6250000, 8750000, 6250000, 787500, 50625, 99225, 2480625, 27562500, 76562500

Offset

1,1

Comments

Table starts

.....81......324.......1296.........3600.........10000...........22500

....324.....2160......14400........60000........250000..........787500

...1296....14400.....160000......1000000.......6250000........27562500

...3600....60000....1000000......8750000......76562500.......450187500

..10000...250000....6250000.....76562500.....937890625......7353062500

..22500...787500...27562500....450187500....7353062500.....74118870000

..50625..2480625..121550625...2647102500...57648010000....747118209600

..99225..6482700..423536400..11859019200..332052537600...5379251109120

.194481.16941456.1475789056..53128406016.1912622616576..38730607985664

.345744.38723328.4337012736.195165573120.8782450790400.217365657062400

Links

R. H. Hardin, Table of n, a(n) for n = 1..262

Formula

Empirical for column k, apparently a recurrence of order 8*k+8, and a polynomial of degree 4*k+4 plus a quasipolynomial of degree 4*k+2 with period 2:

k=1: [linear recurrence of order 16; also a polynomial of degree 8 plus a quasipolynomial of degree 6 with period 2]

k=2: [order 24; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 2]

k=3: [order 32; also a polynomial of degree 16 plus a quasipolynomial of degree 14 with period 2]

k=4: [order 40; also a polynomial of degree 20 plus a quasipolynomial of degree 18 with period 2]

k=5: [order 48; also a polynomial of degree 24 plus a quasipolynomial of degree 22 with period 2]

k=6: [order 56; also a polynomial of degree 28 plus a quasipolynomial of degree 26 with period 2]

k=7: [order 64; also a polynomial of degree 32 plus a quasipolynomial of degree 30 with period 2]

Example

Some solutions for n=3 k=4
..0..0..0..0..0....0..0..0..2..0....0..0..0..2..0....0..0..0..0..0
..0..0..1..0..2....0..0..1..1..1....0..0..0..0..0....0..2..2..2..2
..0..2..0..2..2....0..2..0..2..1....0..1..0..2..1....1..0..2..1..2
..2..1..2..2..2....0..0..2..2..2....0..0..1..2..2....0..2..2..2..2

Crossrefs

Column 1 is A250427

Sequence in context: A053171 A237412 A237405 * A017162 A250427 A236828

Adjacent sequences: A250440 A250441 A250442 * A250444 A250445 A250446

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2014

Status

approved