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

Author

R. H. Hardin, Jul 12 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 4 of A245163.

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)