%I #13 Mar 14 2015 03:48:41
%S 2,2,3,2,3,4,2,3,4,6,2,3,4,7,9,2,3,4,7,11,13,2,3,4,7,11,17,19,2,3,4,7,
%T 11,18,27,28,2,3,4,7,11,18,29,42,41,2,3,4,7,11,18,29,46,66,60,2,3,4,7,
%U 11,18,29,47,74,104,88,2,3,4,7,11,18,29,47,76,118,163,129,2,3,4,7,11,18,29,47
%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 1,1
%C Table starts
%C ....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C ....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3
%C ....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
%C ....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7
%C ....9...11....11....11....11....11....11....11....11....11....11
%C ...13...17....18....18....18....18....18....18....18....18....18
%C ...19...27....29....29....29....29....29....29....29....29....29
%C ...28...42....46....47....47....47....47....47....47....47....47
%C ...41...66....74....76....76....76....76....76....76....76....76
%C ...60..104...118...122...123...123...123...123...123...123...123
%C ...88..163...189...197...199...199...199...199...199...199...199
%C ..129..256...303...317...321...322...322...322...322...322...322
%C ..189..402...485...511...519...521...521...521...521...521...521
%C ..277..631...777...824...838...842...843...843...843...843...843
%C ..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364
%C ..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207
%C ..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571
%C .1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778
%C .1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349
%C .2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127
%C Empirical: for n<=2k+1, T(n,k)=A080023(n)=A169985(n), which is A000032(n) for n>=2. - _Danny Rorabaugh_, Mar 13 2015
%H R. H. Hardin, <a href="/A222334/b222334.txt">Table of n, a(n) for n = 1..9501</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)+a(n-3)
%F k=2: a(n) = a(n-1)+a(n-3)+a(n-5)
%F k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)
%F k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)
%F k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)
%F k=6: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)
%F k=7: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)+a(n-15)
%e Some solutions for n=6 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....1....0....1....0....1....0....1....0....0....1....0....1....0....0
%e ..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1
%e ..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0
%e ..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0
%e ..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0
%e ..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0
%Y Column 1 is A000930(n+2).
%Y Column 2 is A222122.
%Y Columns 3 to 7 are A222329 to A222333.
%Y Cf. A000032, A080023, A169985.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 15 2013