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

1,1

Links

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

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)

Example

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

Crossrefs

Column 2 of A228218.

Sequence in context: A082608 A058031 A359726 * A027608 A354657 A003297

Adjacent sequences: A228209 A228210 A228211 * A228213 A228214 A228215

Keyword

nonn

Author

R. H. Hardin, Aug 16 2013

Status

approved