A213114 Number of binary arrays of length n+7 with fewer than 4 ones in any length 8 subsequence (=less than 50% duty cycle)

93, 151, 252, 424, 714, 1198, 1996, 3292, 5359, 8758, 14401, 23772, 39313, 65046, 107572, 177700, 293113, 483115, 796360, 1313385, 2167141, 3576909, 5904270, 9745234, 16082476, 26536889, 43783532, 72238736, 119193082, 196678607

Offset

1,1

Comments

Column 4 of A213118

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-3) +a(n-6) +a(n-7) +7*a(n-8) +a(n-9) -6*a(n-11) -3*a(n-12) -a(n-13) -5*a(n-14) -a(n-15) -21*a(n-16) -13*a(n-17) -5*a(n-18) +14*a(n-19) +9*a(n-20) -a(n-21) +10*a(n-22) +35*a(n-24) +22*a(n-25) +5*a(n-26) -20*a(n-27) -9*a(n-28) -a(n-29) -10*a(n-30) -a(n-31) -35*a(n-32) -13*a(n-33) +15*a(n-35) +3*a(n-36) +5*a(n-38) +a(n-39) +21*a(n-40) +a(n-41) -6*a(n-43) -a(n-46) -7*a(n-48) +a(n-49) +a(n-51) +a(n-56)

Example

Some solutions for n=3
..1....0....1....0....1....1....1....1....0....1....1....1....0....0....0....0
..0....0....0....1....1....0....1....1....1....0....1....0....0....1....0....0
..0....1....0....0....0....1....1....0....0....0....0....0....1....1....0....1
..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....1....1....0....0....0....1....0....1
..0....1....1....0....0....0....0....0....1....0....0....0....0....0....0....1
..0....0....0....0....0....1....0....0....0....0....1....0....1....0....1....0
..0....0....1....0....0....0....0....0....0....1....0....0....0....0....1....0
..1....0....0....0....1....0....0....1....0....0....0....1....0....0....0....0
..1....1....1....0....0....1....1....1....1....0....1....0....1....0....0....0

Crossrefs

Sequence in context: A153684 A048257 A255991 * A250366 A306540 A044425

Adjacent sequences: A213111 A213112 A213113 * A213115 A213116 A213117

Keyword

nonn

Author

R. H. Hardin Jun 05 2012

Status

approved