A222148 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,-2,1

2, 4, 8, 15, 27, 47, 79, 131, 216, 355, 582, 952, 1554, 2531, 4114, 6679, 10835, 17568, 28474, 46136, 74732, 121021, 195940, 317190, 513415, 830965, 1344839, 2176388, 3521960, 5699251, 9222308, 14922891, 24146832, 39071752, 63221132, 102296095

Offset

1,1

Comments

Column 3 of A222153

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 6*a(n-1) -14*a(n-2) +15*a(n-3) -5*a(n-4) -4*a(n-5) +4*a(n-6) +a(n-7) -12*a(n-8) +27*a(n-9) -25*a(n-10) +a(n-11) +14*a(n-12) -7*a(n-13) -3*a(n-15) +7*a(n-16) -13*a(n-17) +24*a(n-18) -21*a(n-19) +8*a(n-21) +6*a(n-22) -17*a(n-23) +13*a(n-24) -14*a(n-25) +21*a(n-26) -7*a(n-27) -11*a(n-28) +10*a(n-29) -7*a(n-30) +13*a(n-31) -17*a(n-32) -a(n-33) +16*a(n-34) -3*a(n-35) -4*a(n-36) -a(n-37) +3*a(n-38) +4*a(n-39) -13*a(n-40) +7*a(n-42) +a(n-43) +3*a(n-46) -2*a(n-47) -5*a(n-48) -a(n-49) +a(n-50) +a(n-51) +a(n-52) +a(n-53) +a(n-54)

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
..1....0....0....0....0....0....1....1....1....1....1....0....0....1....1....0
..0....0....1....1....0....0....0....0....0....0....0....1....0....0....0....1
..0....0....0....0....1....0....1....0....0....1....1....0....0....0....0....0
..0....0....0....0....0....0....0....0....1....0....0....0....0....0....0....0
..0....1....0....0....0....1....1....0....0....1....0....0....0....1....0....0
..0....0....1....0....1....0....0....1....1....0....1....1....0....0....0....0
..1....1....0....0....0....0....0....0....0....0....0....0....1....0....1....0
..0....0....1....1....1....1....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....0....0....1....1....0....0....0....0....1....1....0....1

Crossrefs

Sequence in context: A328087 A001523 A222039 * A222040 A222149 A222041

Adjacent sequences: A222145 A222146 A222147 * A222149 A222150 A222151

Keyword

nonn

Author

R. H. Hardin Feb 09 2013

Status

approved