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

1,1

Comments

Column 1 of A251428.

Links

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

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)

Example

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

Crossrefs

Cf. A251428.

Sequence in context: A088240 A168457 A045895 * A226393 A371375 A198532

Adjacent sequences: A251418 A251419 A251420 * A251422 A251423 A251424

Keyword

nonn

Author

R. H. Hardin, Dec 02 2014

Status

approved