A221963 Number of -4..4 arrays of length n with the sum ahead of each element differing from the sum following that element by 4 or less.

9, 81, 369, 2241, 12609, 73089, 419841, 2419713, 13930497, 80230401, 462012417, 2660655105, 15322038273, 88236228609, 508131934209, 2926215692289, 16851403538433, 97043367329793, 558850475294721, 3218291629752321

Offset

1,1

Comments

Column 4 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..82

Formula

Empirical: a(n) = 5*a(n-1) + 8*a(n-2) - 20*a(n-3) - 8*a(n-4) + 16*a(n-5).

Empirical g.f.: 9*x*(1 - 2*x)*(1 + 6*x - 8*x^3) / ((1 - x)*(1 + 2*x)*(1 - 6*x + 8*x^3)). - Colin Barker, Aug 11 2018

Example

Some solutions for n=6:
.-3...-2....3....2....3...-4....1....1....2....0....0...-1...-3...-4...-2....0
..4....1....3...-1...-3....1...-3....0...-2....1...-3....4....1...-2....4....3
.-3....1...-4...-2....2....4....2....3....0...-4...-2...-4....2....4...-2...-2
..1...-3...-3....2....3...-4....1....0....1...-1....4....1....1...-1...-2...-1
.-2....3....4....1...-4....3...-1....0...-3....3...-2....2...-3....0....3....1
..2...-3....2...-2....2...-3....2....1....2...-2...-1...-2....0...-3....1....0

Crossrefs

Cf. A221967.

Sequence in context: A208370 A207422 A207737 * A207742 A207719 A167717

Adjacent sequences: A221960 A221961 A221962 * A221964 A221965 A221966

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved