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%I #4 Feb 03 2013 07:25:19
%S 2,2,3,2,3,4,2,3,4,6,2,3,4,6,10,2,3,4,6,10,15,2,3,4,6,10,15,22,2,3,4,
%T 6,10,15,22,35,2,3,4,7,10,15,22,36,54,2,3,4,7,11,15,24,36,56,81,2,3,4,
%U 7,11,16,25,39,56,84,125,2,3,4,7,11,16,27,40,60,84,133,193,2,3,4,7,11,16,27
%N T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,4,6,4,1
%C Table starts
%C ...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2
%C ...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3
%C ...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4
%C ...6...6...6...6...6...7...7...7...7...7...8...8...8...8...8...8...8...8...8
%C ..10..10..10..10..10..11..11..11..11..11..12..12..12..12..12..12..12..12..12
%C ..15..15..15..15..15..16..16..16..16..16..17..17..17..17..17..17..17..17..17
%C ..22..22..22..24..25..27..27..27..27..27..29..29..29..29..29..29..29..29..29
%C ..35..36..36..39..40..43..43..43..43..43..46..46..46..46..46..46..46..46..46
%C ..54..56..56..60..61..65..65..67..68..68..73..73..73..73..73..73..73..73..73
%C ..81..84..84..96.100.108.108.110.111.112.120.120.120.120.120.120.120.120.120
%C .125.133.135.154.160.172.172.175.176.177.189.189.190.190.190.190.190.190.191
%C .193.208.211.240.248.268.271.280.283.285.302.303.305.306.306.306.306.307.308
%H R. H. Hardin, <a href="/A221999/b221999.txt">Table of n, a(n) for n = 1..677</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +2*a(n-3) -a(n-4) -a(n-6) +a(n-7)
%F k=2: a(n) = a(n-1) +3*a(n-3) -2*a(n-4) -3*a(n-6) +2*a(n-7) +a(n-9)
%F k=3: [order 31]
%F k=4: [order 54]
%e Some solutions for n=7 k=4, one extended zero followed by filtered positions
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....1....1....1....0....0....0....0....1....0....0....0....0....0....0
%e ..1....1....0....0....0....1....0....0....1....0....1....0....0....0....1....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....1....0....0....0
%e ..0....1....0....0....0....0....1....1....0....1....0....0....0....0....1....0
%e ..0....0....0....1....0....0....0....0....0....0....1....0....0....0....0....1
%e ..0....0....0....0....1....0....0....0....1....0....0....0....0....1....0....0
%e ..0....1....0....0....0....1....0....1....0....0....0....0....1....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 03 2013
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