A212404 Number of binary arrays of length 2*n+2 with no more than n ones in any length 2n subsequence (=50% duty cycle)

8, 33, 132, 527, 2104, 8402, 33560, 134075, 535728, 2140910, 8556568, 34201078, 136713872, 546528612, 2184925808, 8735357267, 34925461088, 139642914902, 558353310488, 2232601256162, 8927375430608, 35698163696252, 142750104755408

Offset

1,1

Comments

Row 3 of A212402

Links

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

Formula

Recurrence (for n>4): (n-4)*n*a(n) = 2*(n-1)*(4*n-15)*a(n-1) - 8*(n-3)*(2*n-5)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 2^(2*n+1) + C(2*n-2,n). - Vaclav Kotesovec, Oct 28 2012

Example

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

Mathematica

Flatten[{8, 33, RecurrenceTable[{(n-4)*n*a[n]==2*(n-1)*(4*n-15)*a[n-1]-8*(n-3)*(2*n-5)*a[n-2], a[3]==132, a[4]==527}, a, {n, 3, 20}]}] (* Vaclav Kotesovec, Oct 19 2012 *)
Table[2^(2*n+1)+Binomial[2*n-2, n], {n, 1, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)

Crossrefs

Sequence in context: A222346 A317017 A283544 * A048877 A349101 A297683

Adjacent sequences: A212401 A212402 A212403 * A212405 A212406 A212407

Keyword

nonn

Author

R. H. Hardin May 14 2012

Status

approved