A211498 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 three distinct values for every i<=n and j<=n.

38, 84, 166, 318, 600, 1126, 2116, 3988, 7550, 14368, 27464, 52778, 101788, 197248, 383262, 747696, 1461488, 2866146, 5628484, 11082744, 21842862, 43143256, 85269208, 168824386, 334397804, 663306880, 1316099966, 2614415120, 5194474528

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 25*a(n-3) + 16*a(n-4) + 46*a(n-5) - 48*a(n-6) - 26*a(n-7) + 36*a(n-8) + 4*a(n-9) - 8*a(n-10).

Empirical g.f.: 2*x*(19 - 34*x - 123*x^2 + 218*x^3 + 244*x^4 - 426*x^5 - 167*x^6 + 284*x^7 + 36*x^8 - 60*x^9) / ((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:
.-3....2....0....2...-1...-1...-1....0....0...-3....1....3....2....0...-2....3
.-2....1....2...-2....0....1....1...-2....1....3...-1....1...-2....2....0....0
.-1....0...-2....2....1....0....0....0....2....0....1....3....0...-2....2....3
..0....1....2...-2....2...-1....1....1....1...-3....0....1...-2....0...-2....0
..1....2....0....0....3....0...-1....0....0....3...-1...-1....2....2....0....3
..0....1...-1...-2....2...-1....0....1...-1....0....0....1...-2...-2...-2....0

Crossrefs

Sequence in context: A043244 A044024 A133529 * A244733 A044176 A044557

Adjacent sequences: A211495 A211496 A211497 * A211499 A211500 A211501

Keyword

nonn

Author

R. H. Hardin, Apr 13 2012

Status

approved