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A217839 T(n,k)=Number of n element 0..1 arrays with each element the minimum of k adjacent elements of a random 0..1 array of n+k-1 elements.

%I A217839 #6 Jul 22 2025 23:42:55
%S A217839 2,2,4,2,4,8,2,4,7,16,2,4,7,12,32,2,4,7,11,21,64,2,4,7,11,17,37,128,2,
%T A217839 4,7,11,16,27,65,256,2,4,7,11,16,23,44,114,512,2,4,7,11,16,22,34,72,
%U A217839 200,1024,2,4,7,11,16,22,30,52,117,351,2048,2,4,7,11,16,22,29,42,81,189,616
%N A217839 T(n,k)=Number of n element 0..1 arrays with each element the minimum of k adjacent elements of a random 0..1 array of n+k-1 elements.
%C A217839 Table starts
%C A217839 .....2....2....2....2...2...2...2...2...2...2...2...2...2...2
%C A217839 .....4....4....4....4...4...4...4...4...4...4...4...4...4...4
%C A217839 .....8....7....7....7...7...7...7...7...7...7...7...7...7...7
%C A217839 ....16...12...11...11..11..11..11..11..11..11..11..11..11..11
%C A217839 ....32...21...17...16..16..16..16..16..16..16..16..16..16..16
%C A217839 ....64...37...27...23..22..22..22..22..22..22..22..22..22..22
%C A217839 ...128...65...44...34..30..29..29..29..29..29..29..29..29..29
%C A217839 ...256..114...72...52..42..38..37..37..37..37..37..37..37..37
%C A217839 ...512..200..117...81..61..51..47..46..46..46..46..46..46..46
%C A217839 ..1024..351..189..126..91..71..61..57..56..56..56..56..56..56
%C A217839 ..2048..616..305..194.137.102..82..72..68..67..67..67..67..67
%C A217839 ..4096.1081..493..296.205.149.114..94..84..80..79..79..79..79
%C A217839 ..8192.1897..798..450.303.218.162.127.107..97..93..92..92..92
%C A217839 .16384.3329.1292..685.443.316.232.176.141.121.111.107.106.106
%C A217839 .32768.5842.2091.1046.644.452.331.247.191.156.136.126.122.121
%H A217839 R. H. Hardin, <a href="/A217839/b217839.txt">Table of n, a(n) for n = 1..435</a>
%F A217839 Empirical for columns 1-7: a(n) = 2*a(n-1) -a(n-2) +a(n-k-1)
%e A217839 Some solutions for n=8 k=4
%e A217839 ..0....0....1....0....1....0....1....1....0....1....0....0....0....0....0....0
%e A217839 ..1....1....1....1....0....0....1....1....1....0....0....1....0....1....0....0
%e A217839 ..1....1....1....1....0....1....0....1....1....0....1....0....1....0....0....0
%e A217839 ..1....1....0....0....0....0....0....0....0....0....1....0....1....0....1....0
%e A217839 ..1....1....0....0....0....0....0....0....0....0....1....0....1....0....1....1
%e A217839 ..1....1....0....0....0....0....0....0....0....1....1....0....1....0....1....0
%e A217839 ..1....0....0....0....0....0....0....0....0....1....1....0....0....1....1....0
%e A217839 ..0....0....1....0....1....0....1....0....1....1....1....1....0....1....0....0
%Y A217839 Column 2 is A005251(n+3)
%Y A217839 Column 3 is A005252(n+3)
%Y A217839 Column 4 is A005253(n+3)
%Y A217839 Column 5 is A005689(n+6)
%Y A217839 Column 6 is A098574(n+6)
%Y A217839 Diagonal is A000124
%K A217839 nonn,tabl
%O A217839 1,1
%A A217839 _R. H. Hardin_ Oct 12 2012