cp's OEIS Frontend

A221828 T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.

%I A221828 #6 Jul 23 2025 02:16:37
%S A221828 0,0,0,0,3,0,0,16,14,0,0,73,202,64,0,0,333,2879,2930,292,0,0,1519,
%T A221828 40983,115417,41618,1332,0,0,6929,583419,4715043,4755445,592601,6076,
%U A221828 0,0,31607,8304016,192788993,570066685,194407111,8434490,27716,0,0,144177
%N A221828 T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.
%C A221828 Table starts
%C A221828 .0......0..........0............0.............0..............0.............0
%C A221828 .0......3.........16...........73...........333...........1519..........6929
%C A221828 .0.....14........202.........2879.........40983.........583419.......8304016
%C A221828 .0.....64.......2930.......115417.......4715043......192788993....7888216533
%C A221828 .0....292......41618......4755445.....570066685....68573607669.8233561918895
%C A221828 .0...1332.....592601....194407111...68489860450.24121109763712
%C A221828 .0...6076....8434490...7954432829.8224749361083
%C A221828 .0..27716..120053263.325446165881
%C A221828 .0.126428.1708776751
%C A221828 .0.576708
%C A221828 .0
%H A221828 R. H. Hardin, <a href="/A221828/b221828.txt">Table of n, a(n) for n = 1..71</a>
%F A221828 Empirical for col 2: a(n) = 5*a(n-1) -2*a(n-2) for n>3
%F A221828 Empirical for row 2: a(k)=5*a(k-1)-2*a(k-2) for k>4
%e A221828 Some solutions for n=3 k=4
%e A221828 ..0..1..1..0....1..2..1..1....1..1..0..2....0..2..0..1....1..1..1..1
%e A221828 ..1..2..0..1....1..1..2..1....2..1..1..1....2..1..0..1....1..0..1..2
%e A221828 ..2..1..2..1....0..0..1..1....1..1..1..0....1..2..1..1....1..1..2..0
%Y A221828 Column 2 is A060801(n-1)
%K A221828 nonn,tabl
%O A221828 1,5
%A A221828 _R. H. Hardin_ Jan 26 2013