A222124 - OEIS

A222124

Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..5 array extended with zeros and convolved with 1,2,1.

%I #9 Aug 15 2018 12:38:19

%S 2,3,4,8,12,19,31,48,79,126,201,323,516,827,1324,2120,3396,5436,8706,

%T 13940,22323,35748,57240,91661,146778,235035,376367,602677,965074,

%U 1545383,2474634,3962658,6345442,10161019,16270937,26054807,41721820

%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..5 array extended with zeros and convolved with 1,2,1.

%C Column 5 of A222127.

%H R. H. Hardin, <a href="/A222124/b222124.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-8) + a(n-10) + 2*a(n-12) - a(n-13).

%F Empirical g.f.: x*(1 + x + x^2)*(2 - x + 3*x^3 - 2*x^4 + 3*x^6 - 2*x^7 + x^8 + 2*x^9 - x^10) / (1 - x - x^3 - x^5 - x^8 - x^10 - 2*x^12 + x^13). - _Colin Barker_, Aug 15 2018

%e Some solutions for n=7, 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....1....0....1....1....1....1....0....0....0....0....0....0....0....0....0

%e ..0....0....1....0....0....0....0....0....0....1....0....1....0....1....1....0

%e ..0....0....0....0....1....0....0....0....0....0....1....0....0....0....0....0

%e ..0....0....1....0....0....1....0....0....1....0....0....0....1....0....0....0

%e ..0....1....0....0....0....0....0....0....0....0....0....0....0....1....1....1

%e ..1....0....0....0....1....1....1....0....0....0....1....1....1....0....0....0

%e ..0....0....1....1....0....0....0....1....0....0....0....0....0....0....1....1

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%Y Cf. A222127.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 08 2013