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A222333 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..7 array extended with zeros and convolved with 1,1.

%I A222333 #8 Mar 15 2018 05:21:42
%S A222333 2,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2206,3569,5773,9339,
%T A222333 15108,24440,39537,63959,103467,167379,270770,438026,708597,1146301,
%U A222333 1854377,2999835,4852848,7850477,12699756,20544460,33234877,53764229
%N A222333 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..7 array extended with zeros and convolved with 1,1.
%C A222333 Column 7 of A222334.
%H A222333 R. H. Hardin, <a href="/A222333/b222333.txt">Table of n, a(n) for n = 1..210</a>
%F A222333 Empirical: 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).
%F A222333 Empirical g.f.: x*(2 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14) / (1 - x - x^3 - x^5 - x^7 - x^9 - x^11 - x^13 - x^15). - _Colin Barker_, Mar 15 2018
%e A222333 Some solutions for n=6, one extended zero followed by filtered positions:
%e A222333 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A222333 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A222333 ..0....0....1....1....0....1....0....0....0....0....0....0....0....1....1....0
%e A222333 ..0....0....0....0....0....0....0....0....1....0....1....1....1....0....0....0
%e A222333 ..1....0....1....1....1....0....0....0....0....0....0....0....0....0....0....1
%e A222333 ..0....1....0....0....0....0....0....0....0....0....0....1....0....0....0....0
%e A222333 ..1....0....0....1....0....0....0....1....0....0....0....0....1....0....1....0
%e A222333 ..0....0....0....0....0....0....1....0....0....0....1....0....0....1....0....1
%Y A222333 Cf. A222334.
%K A222333 nonn
%O A222333 1,1
%A A222333 _R. H. Hardin_, Feb 15 2013