A212398 Number of binary arrays of length n+7 with no more than 4 ones in any length 8 subsequence (=50% duty cycle)

163, 291, 527, 959, 1747, 3179, 5769, 10425, 18729, 33706, 60797, 109800, 198415, 358592, 647959, 1170415, 2113372, 3815438, 6888722, 12439093, 22463681, 40568913, 73266801, 132315810, 238948339, 431506179, 779231793, 1407175435

Offset

1,1

Comments

Column 4 of A212402

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-4) -a(n-6) +3*a(n-7) +8*a(n-8) -8*a(n-10) -8*a(n-11) -10*a(n-12) -5*a(n-13) +8*a(n-14) -2*a(n-15) -28*a(n-16) -15*a(n-17) +25*a(n-18) +24*a(n-19) +28*a(n-20) +24*a(n-21) -19*a(n-22) -18*a(n-23) +51*a(n-24) +40*a(n-25) -55*a(n-26) -16*a(n-27) -55*a(n-28) -45*a(n-29) +51*a(n-30) +36*a(n-31) -61*a(n-32) -45*a(n-33) +70*a(n-34) -16*a(n-35) +67*a(n-36) +40*a(n-37) -70*a(n-38) -19*a(n-39) +56*a(n-40) +24*a(n-41) -58*a(n-42) +24*a(n-43) -56*a(n-44) -15*a(n-45) +56*a(n-46) -2*a(n-47) -28*a(n-48) -5*a(n-49) +28*a(n-50) -8*a(n-51) +28*a(n-52) -28*a(n-54) +3*a(n-55) +8*a(n-56) -8*a(n-58) -8*a(n-60) +a(n-61) +8*a(n-62) -a(n-64) +a(n-66) +a(n-68) -a(n-70)

Example

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

Crossrefs

Sequence in context: A142534 A142695 A142772 * A157952 A306931 A142427

Adjacent sequences: A212395 A212396 A212397 * A212399 A212400 A212401

Keyword

nonn

Author

R. H. Hardin May 14 2012

Status

approved