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A300089 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%I A300089 #6 Feb 25 2018 06:18:53
%S A300089 1,2,2,3,4,3,5,4,4,5,8,8,1,8,8,13,32,4,4,32,13,21,32,10,25,10,32,21,
%T A300089 34,64,6,50,50,6,64,34,55,256,19,98,415,98,19,256,55,89,256,41,359,
%U A300089 533,533,359,41,256,89,144,512,32,766,3089,1822,3089,766,32,512,144,233,2048,106
%N A300089 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C A300089 Table starts
%C A300089 ..1...2..3....5.....8.....13......21........34.........55..........89
%C A300089 ..2...4..4....8....32.....32......64.......256........256.........512
%C A300089 ..3...4..1....4....10......6......19........41.........32.........106
%C A300089 ..5...8..4...25....50.....98.....359.......766.......1932........5677
%C A300089 ..8..32.10...50...415....533....3089.....13808......27523......150838
%C A300089 .13..32..6...98...533...1822...13646.....64560.....292356.....1935206
%C A300089 .21..64.19..359..3089..13646..167131...1179926....7203918....75245386
%C A300089 .34.256.41..766.13808..64560.1179926..14634300..102798960..1708342471
%C A300089 .55.256.32.1932.27523.292356.7203918.102798960.1518807971.32115302281
%H A300089 R. H. Hardin, <a href="/A300089/b300089.txt">Table of n, a(n) for n = 1..220</a>
%F A300089 Empirical for column k:
%F A300089 k=1: a(n) = a(n-1) +a(n-2)
%F A300089 k=2: a(n) = 8*a(n-3) for n>4
%F A300089 k=3: [order 20] for n>21
%F A300089 k=4: [order 59] for n>61
%e A300089 Some solutions for n=5 k=4
%e A300089 ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
%e A300089 ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
%e A300089 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
%e A300089 ..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
%e A300089 ..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
%Y A300089 Column 1 is A000045(n+1).
%Y A300089 Column 2 is A096252(n-1).
%K A300089 nonn,tabl
%O A300089 1,2
%A A300089 _R. H. Hardin_, Feb 24 2018