

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


8



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
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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



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



KEYWORD



AUTHOR



STATUS

approved



