A245159 Number of length n 0..4 arrays with new values introduced in order from both ends.

1, 1, 2, 4, 9, 23, 65, 199, 654, 2296, 8568, 33794, 140039, 605869, 2718531, 12564289, 59419764, 285878342, 1392536354, 6842206084, 33819153429, 167827213315, 835048228437, 4162123757579, 20768689294634, 103709892420388

Offset

1,3

Links

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

Formula

Empirical: a(n) = 17*a(n-1) - 118*a(n-2) + 434*a(n-3) - 913*a(n-4) + 1097*a(n-5) - 696*a(n-6) + 180*a(n-7) for n>8.

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

G.f.: x*(1 - 16*x + 103*x^2 - 346*x^3 + 656*x^4 - 710*x^5 + 425*x^6 - 124*x^7) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 5*x)).

a(n) = (-3375 - 525*2^(4+n) - 1300*3^n + 3*5^n + 100*(297+9*2^(2+n) + 2*3^n)*n) / 43200.

(End)

Example

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

Crossrefs

Column 4 of A245163.

Sequence in context: A014137 A377409 A245158 * A245160 A245161 A245162

Adjacent sequences: A245156 A245157 A245158 * A245160 A245161 A245162

Keyword

nonn

Author

R. H. Hardin, Jul 12 2014

Status

approved