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A300215 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%I A300215 #4 Feb 28 2018 14:22:54
%S A300215 1,2,2,4,8,4,8,32,32,8,16,128,228,128,16,32,512,1651,1651,512,32,64,
%T A300215 2048,11965,22194,11965,2048,64,128,8192,86775,298600,298600,86775,
%U A300215 8192,128,256,32768,629440,4023881,7452385,4023881,629440,32768,256,512,131072
%N A300215 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C A300215 Table starts
%C A300215 ...1......2........4..........8............16..............32
%C A300215 ...2......8.......32........128...........512............2048
%C A300215 ...4.....32......228.......1651.........11965...........86775
%C A300215 ...8....128.....1651......22194........298600.........4023881
%C A300215 ..16....512....11965.....298600.......7452385.......186427449
%C A300215 ..32...2048....86775....4023881.....186427449......8664017314
%C A300215 ..64...8192...629440...54246856....4666136435....402932952786
%C A300215 .128..32768..4566023..731384148..116802113451..18741286700978
%C A300215 .256.131072.33122989.9861234001.2923892905217.871742323938453
%H A300215 R. H. Hardin, <a href="/A300215/b300215.txt">Table of n, a(n) for n = 1..180</a>
%F A300215 Empirical for column k:
%F A300215 k=1: a(n) = 2*a(n-1)
%F A300215 k=2: a(n) = 4*a(n-1)
%F A300215 k=3: [order 8]
%F A300215 k=4: [order 24]
%F A300215 k=5: [order 89]
%e A300215 Some solutions for n=5 k=4
%e A300215 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e A300215 ..0..1..0..1. .0..0..1..1. .1..1..1..1. .1..1..0..1. .0..1..0..0
%e A300215 ..0..0..1..0. .1..0..1..0. .1..0..1..1. .1..1..0..1. .1..1..1..0
%e A300215 ..0..1..1..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .0..1..1..1
%e A300215 ..0..0..1..1. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..1..0
%Y A300215 Column 1 is A000079(n-1).
%Y A300215 Column 2 is A004171(n-1).
%K A300215 nonn,tabl
%O A300215 1,2
%A A300215 _R. H. Hardin_, Feb 28 2018