A251421 Number of length n+2 0..1 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

2, 12, 12, 40, 56, 144, 240, 544, 992, 2112, 4032, 8320, 16256, 33024, 65280, 131584, 261632, 525312, 1047552, 2099200, 4192256, 8392704, 16773120, 33562624, 67100672, 134234112, 268419072, 536903680, 1073709056, 2147549184, 4294901760

Offset: 1

Author

R. H. Hardin, Dec 02 2014

Keywords

• nonn

Comments

Column 1 of A251428.

Examples

			Some solutions for n=10:
..1....0....1....1....0....0....0....1....1....0....1....1....1....0....1....0
..0....1....1....0....1....1....1....0....0....1....0....1....1....1....0....0
..0....1....1....0....1....0....0....0....1....0....0....1....1....0....0....1
..0....1....0....0....1....0....0....1....0....1....1....1....1....0....1....1
..1....1....1....1....1....0....1....0....0....0....0....0....0....1....0....0
..1....1....0....1....1....0....1....0....1....0....1....1....0....0....0....1
..0....1....0....0....0....0....0....1....0....1....0....0....1....0....0....0
..1....1....0....0....0....1....0....1....0....0....1....0....1....1....0....1
..1....1....0....1....0....0....0....0....1....1....0....0....0....1....0....1
..1....1....0....0....0....0....0....0....0....0....0....0....1....0....0....0
..0....1....1....0....0....0....1....1....1....1....1....0....1....1....1....1
..0....0....1....0....1....1....0....0....1....1....0....0....0....1....0....0
		

Links

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

Crossrefs

Cf. A251428.

Formula

Empirical: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3).

Conjectures from Colin Barker, Mar 20 2018: (Start)

G.f.: 2*x*(1 + 4*x - 8*x^2) / ((1 - 2*x)*(1 - 2*x^2)).

a(n) = 2*(2^(n/2) + 2^n) for n even.

a(n) = 2*(2^n - 2^((n-3)/2+1)) for n odd.

(End)