A222127 T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,2,1.

2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 6, 9, 2, 3, 4, 7, 10, 13, 2, 3, 4, 8, 11, 15, 19, 2, 3, 4, 8, 12, 17, 24, 28, 2, 3, 4, 8, 12, 19, 27, 38, 41, 2, 3, 4, 8, 12, 19, 31, 42, 59, 60, 2, 3, 4, 8, 12, 19, 31, 48, 66, 92, 88, 2, 3, 4, 8, 12, 19, 31, 48, 79, 104, 144, 129, 2, 3, 4, 8, 12, 20, 31, 49

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..2801

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3)

k=2: a(n) = a(n-1) +a(n-3) +a(n-6) +a(n-8)

k=3: a(n) = a(n-1) +a(n-3) +a(n-5)

k=4: a(n) = a(n-1) +a(n-3) +2*a(n-5) -a(n-6)

k=5: a(n) = a(n-1) +a(n-3) +a(n-5) +a(n-8) +a(n-10) +2*a(n-12) -a(n-13)

k=6: a(n) = a(n-1) +a(n-3) +a(n-5) +2*a(n-7) -a(n-8) -a(n-14) +a(n-15)

k=7: a(n) = a(n-1) +a(n-3) +a(n-5) +3*a(n-7) -2*a(n-8) -a(n-10) -a(n-12) -2*a(n-14) +a(n-15)

Example

Table starts:
    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2
    3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3
    4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4
    6,  6,  7,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8,  8
    9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
   13, 15, 17, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21
   19, 24, 27, 31, 31, 31, 31, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33
   28, 38, 42, 48, 48, 49, 49, 51, 53, 53, 53, 53, 53, 53, 54, 55, 55, 55, 55
   41, 59, 66, 79, 79, 80, 80, 83, 86, 86, 86, 86, 86, 86, 87, 88, 88, 88, 88
   60, 92,104,126,126,128,128,132,136,137,138,138,138,138,140,142,142,142,142
   88,144,163,200,201,207,207,215,224,224,224,224,224,224,227,230,230,230,230
  129,224,256,322,323,334,334,346,360,360,360,360,360,360,365,369,370,371,371
  ...
Some solutions for n=7 k=4, 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
..1....0....1....0....1....0....0....0....1....0....1....0....0....0....0....0
..0....1....0....0....0....1....0....0....0....0....0....1....0....0....1....1
..0....0....1....0....0....0....1....1....1....0....0....0....0....0....0....0
..1....0....0....0....0....0....0....0....0....1....0....1....0....0....0....1
..0....1....0....0....0....1....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....1....0....0....1....0....0....1....0....0....0
..1....0....1....1....0....1....0....1....0....0....1....0....0....0....1....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Column 1 is A000930(n+2)

Sequence in context: A222111 A222438 A222027 * A221999 A222334 A340716

Adjacent sequences: A222124 A222125 A222126 * A222128 A222129 A222130

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 08 2013

Status

approved