A221965 Number of -6..6 arrays of length n with the sum ahead of each element differing from the sum following that element by 6 or less.

13, 169, 1105, 9633, 78273, 653185, 5407233, 44890625, 372332545, 3089205249, 25628045313, 212618141697, 1763923329025, 14633929146369, 121406394466305, 1007215475032065, 8356090693812225, 69324049716609025, 575128245018558465

Offset

1,1

Comments

Column 6 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..90

Formula

Empirical: a(n) = 7*a(n-1) + 18*a(n-2) - 56*a(n-3) - 48*a(n-4) + 112*a(n-5) + 32*a(n-6) - 64*a(n-7).

Empirical g.f.: 13*x*(1 + 6*x - 24*x^2 - 32*x^3 + 80*x^4 + 32*x^5 - 64*x^6) / ((1 - x)*(1 - 6*x - 24*x^2 + 32*x^3 + 80*x^4 - 32*x^5 - 64*x^6)). - Colin Barker, Aug 14 2018

Example

Some solutions for n=6:
.-3...-6....0...-6....3....0....0....0....0....0....0...-3...-6....3...-6...-6
..3....5...-5...-3....0....3....0...-3...-3...-3...-2....0....1...-3....5....3
.-2...-1....1....5...-3...-3...-1....0....2....3...-3....0...-3....1....0...-3
..3...-3....6...-1....2...-4....4...-4....3....0....6....0....6...-5...-2....4
.-5....3...-3...-1...-4....6...-5....4...-1....2...-5...-1...-2....4....1...-2
..0...-2...-3...-3....5...-1....3...-3....0...-1...-2...-5...-6...-1....1...-3

Crossrefs

Cf. A221967.

Sequence in context: A264367 A015961 A264133 * A206932 A206867 A181220

Adjacent sequences: A221962 A221963 A221964 * A221966 A221967 A221968

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved