A221993 - OEIS

A221993

Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,4,6,4,1.

%I #8 Aug 14 2018 08:57:58

%S 2,3,4,6,10,15,22,36,56,84,133,208,318,495,772,1192,1846,2870,4448,

%T 6886,10686,16576,25679,39819,61763,95732,148415,230158,356829,553197,

%U 857766,1329946,2061917,3196940,4956807,7685148,11915388,18474452,28643620

%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,4,6,4,1.

%C Column 2 of A221999.

%H R. H. Hardin, <a href="/A221993/b221993.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-3) - 2*a(n-4) - 3*a(n-6) + 2*a(n-7) + a(n-9).

%F Empirical g.f.: x*(1 + x + x^2)*(2 - x - 3*x^3 + 2*x^4 + x^6) / (1 - x - 3*x^3 + 2*x^4 + 3*x^6 - 2*x^7 - x^9). - _Colin Barker_, Aug 14 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....0....0....0....1....1....0....0....1....1....0....1....0....0....0....1

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

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

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

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

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

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

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

%Y Cf. A221999.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2013