A213122 Number of binary arrays of length 2*n+4 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

1, 19, 136, 714, 3354, 14946, 64664, 274676, 1152494, 4793874, 19813536, 81495084, 333932596, 1364199604, 5559496912, 22610923448, 91805888342, 372224952818, 1507347830672, 6097720950428, 24644919356012, 99527343620348

Offset: 1

Author

R. H. Hardin Jun 05 2012

Keywords

• nonn

Comments

Row 5 of A213118

Examples

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

Links

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

Formula

Empirical: 3*n*(77*n-237)*a(n) = 2*(924*n^2-3545*n+2311)*a(n-1) - 8*(462*n^2-2131*n+2347)*a(n-2) - 128*(2*n-9)*a(n-3). - Vaclav Kotesovec, Oct 19 2012