A222149 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,-2,1

2, 4, 8, 15, 27, 47, 80, 134, 221, 362, 591, 963, 1567, 2547, 4136, 6711, 10882, 17635, 28565, 46255, 74885, 121219, 196202, 317544, 513901, 831639, 1345780, 2177711, 3523841, 5701972, 9226323, 14928923, 24156029, 39085936, 63243204, 102330696

Offset

1,1

Comments

Column 4 of A222153

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +49*a(n-3) -49*a(n-4) +21*a(n-5) +7*a(n-6) -13*a(n-7) +8*a(n-8) -16*a(n-9) +46*a(n-10) -72*a(n-11) +56*a(n-12) -13*a(n-13) -6*a(n-14) -a(n-15) +a(n-16) +11*a(n-17) -21*a(n-18) +11*a(n-19) +28*a(n-20) -61*a(n-21) +56*a(n-22) -40*a(n-23) +30*a(n-24) -7*a(n-25) -22*a(n-26) +47*a(n-27) -80*a(n-28) +112*a(n-29) -130*a(n-30) +128*a(n-31) -72*a(n-32) -22*a(n-33) +58*a(n-34) -22*a(n-35) +3*a(n-36) -42*a(n-37) +104*a(n-38) -123*a(n-39) +42*a(n-40) +78*a(n-41) -90*a(n-42) +4*a(n-43) +43*a(n-44) -28*a(n-45) +4*a(n-46) +5*a(n-47) +26*a(n-48) -84*a(n-49) +74*a(n-50) +11*a(n-51) -43*a(n-52) +14*a(n-53) -7*a(n-54) +11*a(n-55) -3*a(n-56) +14*a(n-57) -34*a(n-58) +3*a(n-59) +29*a(n-60) -6*a(n-61) -7*a(n-62) +a(n-63) -9*a(n-64) +19*a(n-65) -3*a(n-66) -14*a(n-67) -6*a(n-68) +7*a(n-69) +6*a(n-70) -2*a(n-73) +5*a(n-74) +3*a(n-75) -6*a(n-76) -6*a(n-77) -a(n-78) +a(n-79) +a(n-80) +a(n-81) +a(n-82) +a(n-83) +2*a(n-84) -a(n-86)

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

Crossrefs

Sequence in context: A222039 A222148 A222040 * A222041 A222042 A222150

Adjacent sequences: A222146 A222147 A222148 * A222150 A222151 A222152

Keyword

nonn

Author

R. H. Hardin Feb 09 2013

Status

approved