A211499 Number of -3..3 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 one or three distinct values for every i<=n and j<=n.

39, 97, 207, 429, 869, 1733, 3449, 6815, 13487, 26619, 52629, 104001, 205793, 407403, 807279, 1600955, 3176941, 6309945, 12537913, 24933779, 49598943, 98736499, 196590789, 391673497, 780437073, 1555911947, 3102177679, 6187923707

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 23*a(n-3) - 9*a(n-4) + 62*a(n-5) - 2*a(n-6) - 74*a(n-7) + 10*a(n-8) + 40*a(n-9) - 4*a(n-10) - 8*a(n-11).

Empirical g.f.: x*(39 - 20*x - 318*x^2 + 123*x^3 + 922*x^4 - 232*x^5 - 1170*x^6 + 164*x^7 + 632*x^8 - 40*x^9 - 120*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 4*x^2 + 2*x^4)). - Colin Barker, Jul 18 2018

Example

Some solutions for n=5:
.-1...-3....0...-2....3....3...-1...-1....1....1...-1....1...-1...-1....0...-3
..1....0....0....2....1....0...-2....0...-2....0....0....3....1...-2....0...-2
.-1....0....0....0....3...-3...-1....2....1....1....2....1....0...-1....0...-1
.-3....3....3....2...-2....3....0....0....3....0....0....3....1....0....3...-2
.-1....0....0....0....3....0....2....2....1...-1...-1....1....0...-1....0...-1
..1....0...-3...-1...-2....3....0...-2...-2....1....0...-2...-1....0....0...-2

Crossrefs

Sequence in context: A044025 A062668 A158339 * A126077 A276401 A044226

Adjacent sequences: A211496 A211497 A211498 * A211500 A211501 A211502

Keyword

nonn

Author

R. H. Hardin, Apr 13 2012

Status

approved