cp's OEIS Frontend

A222334 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.

%I A222334 #15 Jun 02 2025 08:25:33
%S A222334 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 A222334 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 A222334 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 A222334 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 A222334 Table starts
%C A222334 ....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A222334 ....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3
%C A222334 ....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4
%C A222334 ....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7
%C A222334 ....9...11....11....11....11....11....11....11....11....11....11
%C A222334 ...13...17....18....18....18....18....18....18....18....18....18
%C A222334 ...19...27....29....29....29....29....29....29....29....29....29
%C A222334 ...28...42....46....47....47....47....47....47....47....47....47
%C A222334 ...41...66....74....76....76....76....76....76....76....76....76
%C A222334 ...60..104...118...122...123...123...123...123...123...123...123
%C A222334 ...88..163...189...197...199...199...199...199...199...199...199
%C A222334 ..129..256...303...317...321...322...322...322...322...322...322
%C A222334 ..189..402...485...511...519...521...521...521...521...521...521
%C A222334 ..277..631...777...824...838...842...843...843...843...843...843
%C A222334 ..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364
%C A222334 ..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207
%C A222334 ..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571
%C A222334 .1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778
%C A222334 .1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349
%C A222334 .2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127
%C A222334 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 A222334 R. H. Hardin, <a href="/A222334/b222334.txt">Table of n, a(n) for n = 1..9501</a>
%F A222334 Empirical for column k:
%F A222334 k=1: a(n) = a(n-1)+a(n-3)
%F A222334 k=2: a(n) = a(n-1)+a(n-3)+a(n-5)
%F A222334 k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)
%F A222334 k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)
%F A222334 k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)
%F A222334 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 A222334 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 A222334 Some solutions for n=6 k=4, one extended zero followed by filtered positions
%e A222334 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A222334 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A222334 ..0....0....1....0....1....0....1....0....1....0....0....1....0....1....0....0
%e A222334 ..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1
%e A222334 ..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0
%e A222334 ..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0
%e A222334 ..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0
%e A222334 ..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0
%Y A222334 Column 1 is A000930(n+2).
%Y A222334 Column 2 is A222122.
%Y A222334 Columns 3 to 7 are A222329 to A222333.
%Y A222334 Cf. A000032, A080023, A169985.
%K A222334 nonn,tabl
%O A222334 1,1
%A A222334 _R. H. Hardin_ Feb 15 2013