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

Author

R. H. Hardin, Nov 22 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A250427

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]