A221962 Number of -3..3 arrays of length n with the sum ahead of each element differing from the sum following that element by 3 or less.

7, 49, 175, 833, 3647, 16513, 73983, 332801, 1495039, 6719489, 30195711, 135700481, 609828863, 2740551681, 12315918335, 55347249153, 248728256511, 1117774675969, 5023233736703, 22574207598593, 101447567933439, 455901232234497

Offset

1,1

Comments

Column 3 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

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

Empirical g.f.: 7*x*(1 + 4*x - 4*x^2 - 8*x^3) / ((1 + x)*(1 - 4*x - 4*x^2 + 8*x^3)). - Colin Barker, Aug 11 2018

Example

Some solutions for n=6:
..1...-3....1....0...-2....2...-3...-2....1....1....1....0...-3...-2....2....2
.-2...-1....1....1....0...-2....2....1....0...-3...-2....0....0....2...-2....0
..2....2...-3...-2....3...-1....1....0....0....1....3....0....1....2....0....0
.-2...-2....0....3...-2....1...-1....3...-1....0....0....0...-1...-2....1...-3
.-2....1....0...-2....2....2....1...-3....3...-1....1....2....0....2...-2....2
..1...-1....1...-1...-2...-1...-2...-1...-3....1....0...-1...-1...-2....3....0

Crossrefs

Cf. A221967.

Sequence in context: A262269 A163827 A206989 * A373684 A294292 A015953

Adjacent sequences: A221959 A221960 A221961 * A221963 A221964 A221965

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved