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A297224 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

%I A297224 #4 Dec 27 2017 15:38:02
%S A297224 1,2,1,3,4,1,4,8,9,1,6,16,24,19,1,9,33,57,68,41,1,13,69,182,207,196,
%T A297224 88,1,19,145,535,997,751,564,189,1,28,300,1513,4210,5570,2720,1620,
%U A297224 406,1,41,624,4415,16658,33158,30946,9861,4660,872,1,60,1300,12832,68769,178469
%N A297224 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.
%C A297224 Table starts
%C A297224 .1...2.....3......4.......6.........9.........13..........19............28
%C A297224 .1...4.....8.....16......33........69........145.........300...........624
%C A297224 .1...9....24.....57.....182.......535.......1513........4415.........12832
%C A297224 .1..19....68....207.....997......4210......16658.......68769........284867
%C A297224 .1..41...196....751....5570.....33158.....178469.....1051514.......6152761
%C A297224 .1..88...564...2720...30946....261939....1918732....16176806.....134671502
%C A297224 .1.189..1620...9861..171851...2063378...20599895...248421807....2936448567
%C A297224 .1.406..4660..35741..955316..16277793..221333623..3819208252...64142817874
%C A297224 .1.872.13396.129540.5308160.128351805.2377449633.58680928294.1400212345305
%H A297224 R. H. Hardin, <a href="/A297224/b297224.txt">Table of n, a(n) for n = 1..611</a>
%F A297224 Empirical for column k:
%F A297224 k=1: a(n) = a(n-1)
%F A297224 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F A297224 k=3: a(n) = a(n-1) +4*a(n-2) +4*a(n-3)
%F A297224 k=4: a(n) = a(n-1) +6*a(n-2) +11*a(n-3) +6*a(n-4) +a(n-5)
%F A297224 k=5: [order 9]
%F A297224 k=6: [order 11] for n>13
%F A297224 k=7: [order 16] for n>21
%F A297224 Empirical for row n:
%F A297224 n=1: a(n) = a(n-1) +a(n-3)
%F A297224 n=2: a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +a(n-5) -a(n-6)
%F A297224 n=3: [order 13]
%F A297224 n=4: [order 27]
%F A297224 n=5: [order 60]
%e A297224 Some solutions for n=5 k=4
%e A297224 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..0
%e A297224 ..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..0
%e A297224 ..0..1..0..0. .0..1..0..0. .1..0..0..0. .1..0..0..0. .0..1..0..0
%e A297224 ..0..1..1..0. .1..0..0..1. .0..1..1..0. .0..0..1..1. .1..0..0..0
%e A297224 ..0..0..0..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..0
%Y A297224 Column 2 is A078039.
%Y A297224 Row 1 is A000930(n+1).
%Y A297224 Row 2 is A264166.
%K A297224 nonn,tabl
%O A297224 1,2
%A A297224 _R. H. Hardin_, Dec 27 2017