A222330 - OEIS

A222330

Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,1.

%I #8 Aug 15 2018 12:38:45

%S 2,3,4,7,11,18,29,47,76,122,197,317,511,824,1328,2141,3451,5563,8967,

%T 14454,23299,37556,60538,97583,157297,253552,408708,658809,1061954,

%U 1711796,2759296,4447793,7169533,11556788,18628738,30028229,48403415

%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,1.

%C Column 4 of A222334.

%H R. H. Hardin, <a href="/A222330/b222330.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-7) + a(n-9).

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

%e Some solutions for n=6, 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 ..1....1....1....1....0....0....0....0....0....1....0....0....0....1....0....0

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

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

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

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

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

%Y Cf. A222334.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2013