A211460 Number of -2..2 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.

21, 53, 121, 259, 549, 1119, 2285, 4575, 9185, 18275, 36437, 72387, 144013, 286211, 569361, 1132703, 2254869, 4490887, 8948013, 17838815, 35573537, 70976563, 141639157, 282775411, 564615853, 1127756979, 2252749969, 4501187503

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 20*a(n-3) - 5*a(n-4) + 45*a(n-5) - 5*a(n-6) - 40*a(n-7) + 6*a(n-8) + 12*a(n-9).

Empirical g.f.: x*(21 - 10*x - 143*x^2 + 51*x^3 + 332*x^4 - 83*x^5 - 312*x^6 + 60*x^7 + 104*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - Colin Barker, Jul 17 2018

Example

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

Crossrefs

Sequence in context: A347837 A304517 A007796 * A354160 A190664 A144302

Adjacent sequences: A211457 A211458 A211459 * A211461 A211462 A211463

Keyword

nonn

Author

R. H. Hardin, Apr 12 2012

Status

approved