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A222332 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 array extended with zeros and convolved with 1,1. 1

%I #8 Aug 16 2018 08:57:56

%S 2,3,4,7,11,18,29,47,76,123,199,322,521,842,1362,2202,3561,5759,9313,

%T 15061,24356,39388,63697,103009,166583,269393,435654,704526,1139338,

%U 1842502,2979638,4818579,7792458,12601724,20379121,32956489,53296222

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

%C Column 6 of A222334.

%H R. H. Hardin, <a href="/A222332/b222332.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) + a(n-11) + a(n-13).

%F 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) / (1 - x - x^3 - x^5 - x^7 - x^9 - x^11 - x^13). - _Colin Barker_, Aug 16 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 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

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

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

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

%Y Cf. A222334.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2013

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Last modified August 5 22:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)