A253468 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally

81, 540, 540, 3640, 800, 3640, 24208, 1400, 1400, 24208, 162016, 3072, 2000, 3072, 162016, 1081504, 8536, 2600, 2600, 8536, 1081504, 7227096, 15888, 5000, 3744, 5000, 15888, 7227096, 48272160, 44464, 7784, 7496, 7496, 7784, 44464, 48272160

Offset

1,1

Comments

Table starts

.........81....540...3640..24208.162016.1081504.7227096.48272160.322493040

........540....800...1400...3072...8536...15888...44464....94416....273808

.......3640...1400...2000...2600...5000....7784...17000....28520.....65000

......24208...3072...2600...3744...7496....8272...15680....31824.....94016

.....162016...8536...5000...7496...8000...12680...20000....33416.....68000

....1081504..15888...7784...8272..12680...12800...20864....36352.....99200

....7227096..44464..17000..15680..20000...20864...32000....41600.....80000

...48272160..94416..28520..31824..33416...36352...41600....59904....119936

..322493040.273808..65000..94016..68000...99200...80000...119936....128000

.2154281664.562320.111464.104272.116360..108800..124544...132352....202880

Links

R. H. Hardin, Table of n, a(n) for n = 1..3360

Formula

Empirical for diagonal and column k:

diagonal: a(n) = 16*a(n-4) for n>5

k=1: a(n) = 2*a(n-1) +27*a(n-2) +30*a(n-3) -7*a(n-4) -8*a(n-5) -75*a(n-6) -48*a(n-7) -16*a(n-8)

k=2: a(n) = 5*a(n-2) +8*a(n-4) -12*a(n-6) for n>7

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

k=4: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8

k=5: a(n) = 5*a(n-2) -4*a(n-4) for n>6

k=6: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8

k=7: a(n) = 5*a(n-2) -4*a(n-4) for n>6

Example

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

Crossrefs

Sequence in context: A235784 A235565 A235560 * A253462 A206512 A235833

Adjacent sequences: A253465 A253466 A253467 * A253469 A253470 A253471

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2015

Status

approved