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A298888 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

%I A298888 #4 Jan 28 2018 08:47:56
%S A298888 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 A298888 13,95,34,73,73,34,95,13,21,177,63,141,123,141,63,177,21,34,359,96,
%U A298888 240,243,243,240,96,359,34,55,705,147,428,444,516,444,428,147,705,55,89,1351,233
%N A298888 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
%C A298888 Table starts
%C A298888 ..0...1...1...2....3....5....8....13....21....34.....55.....89.....144.....233
%C A298888 ..1...3...7..13...23...49...95...177...359...705...1351...2689....5303...10321
%C A298888 ..1...7..15..19...23...34...63....96...147...233....368....588.....933....1500
%C A298888 ..2..13..19..40...73..141..240...428...779..1531...2989...5729...10760...20205
%C A298888 ..3..23..23..73..123..243..444...897..1801..3462...6669..13291...25762...49483
%C A298888 ..5..49..34.141..243..516..814..1646..3312..6565..13040..25941...51679..103895
%C A298888 ..8..95..63.240..444..814.1818..3663..7496.16544..33596..70466..148451..311053
%C A298888 .13.177..96.428..897.1646.3663..7768.17225.39617..83996.184024..411042..903972
%C A298888 .21.359.147.779.1801.3312.7496.17225.41048.95996.221358.505218.1183870.2737277
%H A298888 R. H. Hardin, <a href="/A298888/b298888.txt">Table of n, a(n) for n = 1..312</a>
%F A298888 Empirical for column k:
%F A298888 k=1: a(n) = a(n-1) +a(n-2)
%F A298888 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 A298888 k=3: [order 18] for n>19
%F A298888 k=4: [order 72] for n>73
%e A298888 Some solutions for n=7 k=5
%e A298888 ..0..1..0..0..0. .0..1..0..1..1. .0..0..1..0..1. .0..1..1..0..1
%e A298888 ..0..0..1..1..1. .1..0..0..1..0. .1..0..1..1..0. .1..0..0..0..1
%e A298888 ..0..0..0..0..0. .0..1..1..1..0. .1..0..0..0..1. .1..0..0..0..1
%e A298888 ..1..0..0..0..1. .0..1..1..1..0. .1..0..0..0..1. .0..0..0..0..0
%e A298888 ..1..0..0..0..1. .1..1..1..1..1. .0..0..0..0..0. .1..1..1..0..0
%e A298888 ..0..1..1..0..1. .1..1..0..0..0. .1..1..1..0..0. .0..0..0..0..1
%e A298888 ..1..0..1..0..0. .1..0..1..1..1. .0..0..0..1..0. .1..1..1..0..1
%Y A298888 Column 1 is A000045(n-1).
%Y A298888 Column 2 is A297852.
%Y A298888 Column 3 is A298050.
%Y A298888 Column 4 is A298051.
%K A298888 nonn,tabl
%O A298888 1,5
%A A298888 _R. H. Hardin_, Jan 28 2018