A204076 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
8, 38, 38, 188, 329, 188, 938, 2882, 2882, 938, 4688, 25277, 45056, 25277, 4688, 23438, 221726, 706454, 706454, 221726, 23438, 117188, 1944977, 11081828, 19934369, 11081828, 1944977, 117188, 585938, 17061338, 173848010, 563880962, 563880962
Offset: 1
Examples
Some solutions for n=4 k=3 ..0..0..0..0....0..0..0..0....0..0..1..2....0..0..0..1....0..0..1..2 ..0..0..0..0....1..0..0..0....2..0..0..1....2..0..1..0....2..0..0..1 ..1..0..0..2....2..1..0..0....1..2..0..0....0..2..0..1....0..1..0..0 ..2..1..0..0....2..2..1..0....2..2..2..0....2..0..0..0....0..0..0..0 ..1..2..1..0....2..0..2..1....0..2..2..2....2..2..0..1....2..0..0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..220
Crossrefs
Column 1 is A199213
Formula
Empirical for column k:
k=1: a(n) = (3*5^n+1)/2
k=2: a(n) = 10*a(n-1) -11*a(n-2) +2*a(n-3)
k=3: a(n) = 20*a(n-1) -73*a(n-2) +86*a(n-3) -32*a(n-4)
k=4: a(n) = 32*a(n-1) -55*a(n-2) -1588*a(n-3) +5428*a(n-4) -2664*a(n-5) -3936*a(n-6) +3040*a(n-7) -256*a(n-8)
k=5: (order 13 recurrence)
k=6: (order 29 recurrence)
k=7: (order 55 recurrence)
Comments