A222038 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, 46, 77, 127, 208, 339, 551, 894, 1448, 2344, 3794, 6141, 9940, 16089, 26041, 42145, 68204, 110371, 178602, 289006, 467648, 756702, 1224404, 1981165, 3205633, 5186867, 8392575, 13579526, 21972200, 35551845, 57524194, 93076232

Offset

1,1

Comments

Column 3 of A222043

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

Crossrefs

Sequence in context: A054174 A239890 A331554 * A328087 A001523 A222039

Adjacent sequences: A222035 A222036 A222037 * A222039 A222040 A222041

Keyword

nonn

Author

R. H. Hardin Feb 06 2013

Status

approved