A201082 Number of -2..2 arrays of n elements with first and second differences also in -2..2.

5, 19, 57, 175, 537, 1653, 5089, 15663, 48207, 148375, 456685, 1405633, 4326401, 13316243, 40986117, 126151337, 388281713, 1195093865, 3678384289, 11321714051, 34847150005, 107256185601, 330124252601, 1016090788147, 3127429995345

Offset: 1

Author

R. H. Hardin, Nov 26 2011

Keywords

• nonn

Comments

Column 2 of A201088.

Examples

			Some solutions for n=9:
..0....1....1...-2...-2...-1....2....2....0....2....0....0....0....1...-2....2
..0....0....0...-1....0....0....1....2...-1....2....1....1....2...-1...-2....2
.-1...-2....0...-1....0....0....0....1....0....0....0....0....2...-1...-1....2
.-1...-2....1...-1....0....0....1....1....1....0...-1....1....1....1....0....0
.-1....0....1...-1...-2...-2....0....2....2....1...-2....0....2....1....0....0
..0....0....2....0...-2...-2...-1....2....2....0...-1...-1....1....1...-1...-2
.-1...-1....1...-1...-1...-1...-2....2....2....1....0...-2...-1....1...-1...-2
.-1...-2....0...-1...-2....0...-1....0....1....1....0...-2...-1....0...-1...-1
..0...-2....1...-2...-2...-1...-2....0....0....1....0...-1....0....0....0....1
		

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) -2*a(n-3) -2*a(n-5) -4*a(n-6) +2*a(n-8) +a(n-9).

Empirical g.f.: x*(1 + x)*(5 - x - 4*x^2 - x^3 - 6*x^4 - 3*x^5 + 4*x^6 + 3*x^7) / (1 - 3*x - x^2 + 2*x^3 + 2*x^5 + 4*x^6 - 2*x^8 - x^9). - Colin Barker, Feb 15 2018