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A298259 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

%I A298259 #4 Jan 15 2018 15:00:10
%S A298259 0,0,0,0,1,0,0,3,3,0,0,2,1,2,0,0,11,4,4,11,0,0,13,3,11,3,13,0,0,34,7,
%T A298259 23,23,7,34,0,0,65,14,72,86,72,14,65,0,0,123,35,201,238,238,201,35,
%U A298259 123,0,0,266,89,597,604,895,604,597,89,266,0,0,499,242,1705,2492,3335,3335,2492
%N A298259 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
%C A298259 Table starts
%C A298259 .0...0..0....0....0.....0......0.......0........0.........0.........0
%C A298259 .0...1..3....2...11....13.....34......65......123.......266.......499
%C A298259 .0...3..1....4....3.....7.....14......35.......89.......242.......643
%C A298259 .0...2..4...11...23....72....201.....597.....1705......5141.....15305
%C A298259 .0..11..3...23...86...238....604....2492.....7722.....26880.....93816
%C A298259 .0..13..7...72..238...895...3335...13980....55889....230402....953813
%C A298259 .0..34.14..201..604..3335..13991...70095...331341...1644480...8037526
%C A298259 .0..65.35..597.2492.13980..70095..435534..2412035..14299708..83146969
%C A298259 .0.123.89.1705.7722.55889.331341.2412035.16014301.112395697.777907073
%H A298259 R. H. Hardin, <a href="/A298259/b298259.txt">Table of n, a(n) for n = 1..220</a>
%F A298259 Empirical for column k:
%F A298259 k=1: a(n) = a(n-1)
%F A298259 k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
%F A298259 k=3: [order 18] for n>19
%F A298259 k=4: [order 53] for n>54
%e A298259 Some solutions for n=7 k=4
%e A298259 ..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1
%e A298259 ..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1
%e A298259 ..1..0..1..0. .0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..1..0
%e A298259 ..1..1..0..0. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..1..0..1
%e A298259 ..1..0..1..0. .1..1..1..1. .0..1..1..0. .0..0..0..1. .0..1..0..1
%e A298259 ..0..1..1..0. .1..1..1..1. .1..0..0..1. .0..1..1..0. .1..0..0..1
%e A298259 ..0..0..0..0. .1..1..1..1. .1..1..1..1. .1..1..0..0. .1..1..1..1
%Y A298259 Column 2 is A297870.
%K A298259 nonn,tabl
%O A298259 1,8
%A A298259 _R. H. Hardin_, Jan 15 2018