A230977 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

0, 16, 16, 64, 144, 64, 256, 1024, 1024, 256, 1344, 9216, 13872, 9216, 1344, 7056, 85264, 215296, 215296, 85264, 7056, 34944, 767376, 3512016, 6170256, 3512016, 767376, 34944, 173056, 6885376, 56791296, 190219264, 190219264, 56791296

Offset

1,2

Comments

Table starts

......0.......16..........64...........256.............1344...............7056

.....16......144........1024..........9216............85264.............767376

.....64.....1024.......13872........215296..........3512016...........56791296

....256.....9216......215296.......6170256........190219264.........5771137024

...1344....85264.....3512016.....190219264......11094079744.......630277210000

...7056...767376....56791296....5771137024.....630277210000.....66985909298064

..34944..6885376...916182800..173342326336...35475345905904...7053147648320400

.173056.61968384.14798235904.5217149355664.2001432811365376.744552485586204304

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +20*a(n-3) +25*a(n-4)

k=2: a(n) = 9*a(n-1) -8*a(n-2) +72*a(n-3) +9*a(n-4) -81*a(n-5)

k=3: [order 25]

Example

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

Crossrefs

Sequence in context: A278348 A022350 A226068 * A174683 A174994 A175971

Adjacent sequences: A230974 A230975 A230976 * A230978 A230979 A230980

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 02 2013

Status

approved