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%I #4 Jan 25 2018 08:58:02
%S 1,1,1,1,5,1,1,7,7,1,1,18,5,18,1,1,31,15,15,31,1,1,65,21,34,21,65,1,1,
%T 130,57,77,77,57,130,1,1,253,119,230,336,230,119,253,1,1,519,285,712,
%U 1041,1041,712,285,519,1,1,1018,725,2167,3676,4001,3676,2167,725,1018,1
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1...1....1.....1......1.......1........1........1.........1..........1
%C .1...5...7...18....31.....65.....130......253......519......1018.......2055
%C .1...7...5...15....21.....57.....119......285......725......1833.......4807
%C .1..18..15...34....77....230.....712.....2167.....6694.....20775......64197
%C .1..31..21...77...336...1041....3676....12970....45311....162322.....581460
%C .1..65..57..230..1041...4001...16320....67159...281930...1196239....5097819
%C .1.130.119..712..3676..16320...76983...380106..1892587...9597169...48598454
%C .1.253.285.2167.12970..67159..380106..2232433.13202628..79480110..477560387
%C .1.519.725.6694.45311.281930.1892587.13202628.92349689.659941442.4710349603
%H R. H. Hardin, <a href="/A298727/b298727.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F k=3: [order 17] for n>18
%F k=4: [order 58] for n>60
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e ..1..0..0..1. .0..0..0..0. .0..1..0..1. .0..1..1..0. .0..0..0..0
%e ..1..1..1..0. .1..0..1..0. .1..1..0..1. .0..1..0..1. .0..0..0..0
%e ..0..0..0..0. .1..1..1..0. .0..1..0..1. .1..0..0..1. .0..0..0..0
%e ..1..0..1..0. .0..1..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0
%Y Column 2 is A297937.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 25 2018
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