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

Author

R. H. Hardin Jun 05 2012

Keywords

• nonn

Comments

Column 4 of A213118

Examples

			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
		

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)