A245158 Number of length n 0..3 arrays with new values introduced in order from both ends.

1, 1, 2, 4, 9, 23, 65, 199, 653, 2275, 8313, 31439, 121637, 477307, 1888721, 7509799, 29940861, 119550419, 477742889, 1909988479, 7637856725, 30546970411, 122178444417, 488693854679, 1954733475629, 7818845822083, 31275198738905

Offset

1,3

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>6.

Conjectures from Colin Barker, Nov 03 2018: (Start)

G.f.: x*(1 - 9*x + 29*x^2 - 43*x^3 + 31*x^4 - 11*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).

a(n) = (-64 - 27*2^(2+n) + 4^n + 12*(32+3*2^n)*n) / 576 for n>1.

(End)

Example

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....1....1....1....1....1....1....1....0....0....1....1....1
..0....0....0....1....1....2....0....2....2....0....0....1....0....0....1....2
..0....1....0....1....0....0....1....2....1....2....2....0....0....0....2....1
..1....2....0....2....1....2....1....1....0....1....1....1....0....0....0....1
..0....1....0....1....0....1....0....0....0....1....0....0....0....1....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Column 3 of A245163.

Sequence in context: A164039 A362549 A014137 * A245159 A245160 A245161

Adjacent sequences: A245155 A245156 A245157 * A245159 A245160 A245161

Keyword

nonn

Author

R. H. Hardin, Jul 12 2014

Status

approved