A222334 - OEIS

%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