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A221852 T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.

%I A221852 #6 Jul 23 2025 02:17:12
%S A221852 1,3,1,6,31,1,13,302,306,1,28,3437,10085,2989,1,60,37155,465305,
%T A221852 354670,29135,1,129,406612,19159028,67228149,12277568,283872,1,277,
%U A221852 4434129,811781250,10799370973,9607602488,426752551,2765627,1,595,48397883
%N A221852 T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.
%C A221852 Table starts
%C A221852 .1.......3.........6.........13..........28............60.........129......277
%C A221852 .1......31.......302.......3437.......37155........406612.....4434129.48397883
%C A221852 .1.....306.....10085.....465305....19159028.....811781250.34109464173
%C A221852 .1....2989....354670...67228149.10799370973.1802820316744
%C A221852 .1...29135..12277568.9607602488
%C A221852 .1..283872.426752551
%C A221852 .1.2765627
%C A221852 .1
%H A221852 R. H. Hardin, <a href="/A221852/b221852.txt">Table of n, a(n) for n = 1..40</a>
%e A221852 Some solutions for n=3 k=4
%e A221852 ..0..0..3..1....0..0..0..2....0..1..3..0....0..0..1..1....0..1..1..0
%e A221852 ..0..1..1..1....0..4..1..2....0..0..1..1....0..3..0..1....1..3..0..1
%e A221852 ..1..4..0..0....2..0..0..1....3..1..1..1....0..4..1..1....0..1..4..0
%Y A221852 Column 2 is A220997
%Y A221852 Row 1 is A002478
%K A221852 nonn,tabl
%O A221852 1,2
%A A221852 _R. H. Hardin_ Jan 27 2013