A211526 Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four or five distinct values for every i,j,k<=n.

8, 18, 32, 60, 104, 192, 344, 648, 1208, 2328, 4472, 8760, 17144, 33912, 67064, 133368, 265208, 528888, 1054712, 2106360, 4206584, 8407032, 16801784, 33591288, 67158008, 134291448, 268533752, 537018360, 1073938424, 2147778552, 4295360504

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..69

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Jul 18 2018: (Start)

G.f.: 2*x*(4 - 3*x - 11*x^2 + 6*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2) + 2^(n+1) - 8 for n even.

a(n) = 2*(2^n + 3*2^((n+1)/2) - 4) for n odd.

(End)

Example

Some solutions for n=5:
.-1...-1...-1....0....0...-1....1....0...-1....1....1....1...-1...-1....1....0
..0....1...-1....1...-1....1....1....1....1...-1....1....1....1...-1...-1....1
.-1....0...-1....0....0....1...-1....0....0...-1...-1....1...-1....1....1...-1
..0....1...-1...-1....1...-1...-1....1....1....1...-1....1....0...-1....1....1
..1....0....1....0....0....1....1....0...-1...-1...-1....1...-1....1....1....0
..0....1....1....1...-1....1...-1....1....1...-1....1....1....1...-1....1....1

Crossrefs

Sequence in context: A028563 A171523 A120091 * A211528 A297841 A098944

Adjacent sequences: A211523 A211524 A211525 * A211527 A211528 A211529

Keyword

nonn

Author

R. H. Hardin, Apr 14 2012

Status

approved