A211479 Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two, three or four distinct values for every i<=n and j<=n.

8, 22, 58, 150, 382, 962, 2402, 5958, 14702, 36130, 88498, 216198, 527038, 1282562, 3116738, 7565190, 18345422, 44452642, 107643922, 260526918, 630270622, 1524213890, 3684989858, 8906776518, 21523708718, 52004525602, 125633423218

Offset

1,1

Links

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

Formula

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

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

G.f.: 2*x*(4 - 5*x - 3*x^2) / ((1 - 2*x)*(1 - 2*x - x^2)).

a(n) = -3*2^n + (3-2*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(3+2*sqrt(2)).

(End)

Example

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

Crossrefs

Sequence in context: A211530 A058404 A350123 * A318034 A326162 A126362

Adjacent sequences: A211476 A211477 A211478 * A211480 A211481 A211482

Keyword

nonn

Author

R. H. Hardin, Apr 12 2012

Status

approved