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A298055 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.

%I A298055 #6 May 11 2023 14:37:36
%S A298055 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,19,19,23,5,8,49,23,40,23,49,8,
%T A298055 13,95,34,73,73,34,95,13,21,177,63,141,121,141,63,177,21,34,359,96,
%U A298055 240,231,231,240,96,359,34,55,705,147,428,422,512,422,428,147,705,55,89,1351,233
%N A298055 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.
%C A298055 Table starts
%C A298055 ..0...1...1...2....3....5....8....13....21....34.....55.....89....144.....233
%C A298055 ..1...3...7..13...23...49...95...177...359...705...1351...2689...5303...10321
%C A298055 ..1...7..15..19...23...34...63....96...147...233....368....588....933....1500
%C A298055 ..2..13..19..40...73..141..240...428...779..1531...2989...5729..10760...20205
%C A298055 ..3..23..23..73..121..231..422...865..1729..3286...6319..12563..24164...46151
%C A298055 ..5..49..34.141..231..512..780..1577..3162..6228..12289..24231..47917...95955
%C A298055 ..8..95..63.240..422..780.1708..3362..6794.14943..29523..61474.128150..264417
%C A298055 .13.177..96.428..865.1577.3362..7014.15247.34464..71665.153171.337793..727538
%C A298055 .21.359.147.779.1729.3162.6794.15247.35804.81453.182350.407843.937627.2114521
%H A298055 R. H. Hardin, <a href="/A298055/b298055.txt">Table of n, a(n) for n = 1..337</a>
%F A298055 Empirical for column k:
%F A298055 k=1: a(n) = a(n-1) +a(n-2)
%F A298055 k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
%F A298055 k=3: [order 18] for n>19
%F A298055 k=4: [order 72] for n>73
%e A298055 Some solutions for n=5, k=4
%e A298055 ..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..0..1..0. .0..1..1..1
%e A298055 ..1..0..1..1. .1..0..0..0. .1..1..1..1. .1..0..1..0. .0..0..0..0
%e A298055 ..1..0..0..0. .0..0..1..0. .0..1..1..1. .1..0..0..1. .0..0..0..1
%e A298055 ..0..1..0..1. .1..1..0..0. .1..0..1..0. .0..1..0..1. .1..0..1..0
%e A298055 ..0..1..0..1. .1..0..1..1. .1..0..1..0. .0..1..0..0. .1..0..1..0
%Y A298055 Column 1 is A000045(n-1).
%Y A298055 Column 2 is A297852.
%K A298055 nonn,tabl
%O A298055 1,5
%A A298055 _R. H. Hardin_, Jan 11 2018