A228212 Number of second differences of arrays of length n + 2 of numbers in 0..2.

9, 49, 199, 665, 2059, 6305, 19171, 58025, 175099, 527345, 1586131, 4766585, 14316139, 42981185, 129009091, 387158345, 1161737179, 3485735825, 10458256051, 31376865305, 94134790219, 282412759265, 847255055011, 2541798719465

Offset: 1

Author

R. H. Hardin, Aug 16 2013

Keywords

• nonn

Examples

			Some solutions for n=4:
..3....3...-4....0....1....0...-3...-1...-2....4....0...-4....0....0....3....2
.-1...-2....3....3...-1...-2....2....0....4...-4....0....3...-2...-1....0...-1
.-1...-1....0...-3....0....1...-2....1...-2....4....1....0....0....0...-3....0
..2....1...-2....2....0....1....0...-3...-2...-2...-3...-3....3...-1....3....1
		

Links

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

Crossrefs

Column 2 of A228218.

Formula

Empirical: a(n) = 5*a(n-1) -6*a(n-2) = A001047(n+2) for n>5.

Conjectures from Colin Barker, Sep 09 2018: (Start)

G.f.: x*(9 + 4*x + 8*x^2 - 36*x^3 - 72*x^4) / ((1 - 2*x)*(1 - 3*x)).

a(n) = 3^(2+n) - 2^(2+n) for n>3.

(End)