A230739 T(n,k)=Number of (n+3)X(k+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
2, 8, 8, 30, 66, 30, 102, 244, 244, 102, 348, 2016, 2106, 2016, 348, 1172, 6576, 16536, 16536, 6576, 1172, 3956, 54138, 130446, 320970, 130446, 54138, 3956, 13326, 173428, 1025430, 2382398, 2382398, 1025430, 173428, 13326, 44916, 1427040, 8053490
Offset: 1
Examples
Some solutions for n=3 k=4 ..x..0..x..0..x..2..x....x..0..x..2..x..2..x....x..0..x..0..x..1..x ..1..x..1..x..1..x..0....2..x..1..x..0..x..1....1..x..1..x..2..x..0 ..x..2..x..0..x..1..x....x..0..x..1..x..1..x....x..2..x..0..x..2..x ..1..x..0..x..2..x..0....1..x..0..x..2..x..0....1..x..0..x..2..x..0 ..x..2..x..1..x..1..x....x..2..x..0..x..2..x....x..2..x..1..x..1..x ..1..x..1..x..0..x..0....1..x..2..x..1..x..1....1..x..0..x..0..x..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..199
Formula
Empirical for column k:
k=1: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) +a(n-5)
k=2: a(n) = 31*a(n-2) -126*a(n-4) +42*a(n-6) +79*a(n-8) -a(n-10) +8*a(n-12)
k=3: [order 22]
k=4: [order 50]
Comments