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A222022
Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..3 array extended with zeros and convolved with 1,3,3,1.
1
2, 3, 4, 7, 11, 16, 26, 41, 62, 99, 156, 242, 382, 600, 938, 1475, 2314, 3627, 5696, 8935, 14016, 22000, 34515, 54153, 84981, 133334, 209209, 328278, 515083, 808208, 1268156, 1989823, 3122203, 4899001, 7686907, 12061403, 18925330, 29695352
OFFSET
1,1
COMMENTS
Column 3 of A222027.
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) + a(n-8) - a(n-9) + a(n-11) - a(n-12) - 2*a(n-14) + a(n-15).
Empirical g.f.: x*(2 + x + x^2 - x^3 - 2*x^8 - 2*x^11 - x^12 - x^13 + x^14) / ((1 - x)*(1 + x + x^2)*(1 - x - x^3 - x^6 - x^8 - 2*x^11 + x^12)). - Colin Barker, Aug 14 2018
EXAMPLE
Some solutions for n=7, one extended zero followed by filtered positions:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....0....1....1....0....1....0....1....0....1....0....0....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....1....1....0
..0....1....0....0....1....0....1....0....0....0....0....1....0....0....0....1
..0....0....1....1....0....1....0....0....0....0....1....0....0....1....0....0
..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0
..0....0....1....0....0....1....1....0....0....0....0....0....1....0....0....0
..0....1....0....0....0....0....0....0....0....0....1....1....0....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
CROSSREFS
Cf. A222027.
Sequence in context: A210518 A113435 A367667 * A025048 A017987 A337495
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 05 2013
STATUS
approved