A221966 Number of -7..7 arrays of length n with the sum ahead of each element differing from the sum following that element by 7 or less.

15, 225, 1695, 17025, 159615, 1535745, 14661375, 140355585, 1342437375, 12843782145, 122870296575, 1175482548225, 11245539966975, 107583628673025, 1029227717656575, 9846388295204865, 94198150438322175, 901172262043910145

Offset

1,1

Comments

Column 7 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..67

Formula

Empirical: a(n) = 7*a(n-1) + 32*a(n-2) - 56*a(n-3) - 160*a(n-4) + 112*a(n-5) + 256*a(n-6) - 64*a(n-7) - 128*a(n-8).

Empirical g.f.: 15*x*(1 + 2*x)*(1 - 2*x - 4*x^2)*(1 + 8*x - 16*x^2 - 8*x^3 + 16*x^4) / ((1 + x)*(1 - 2*x)*(1 + 2*x - 4*x^2)*(1 - 8*x - 16*x^2 + 8*x^3 + 16*x^4)). - Colin Barker, Aug 14 2018

Example

Some solutions for n=6:
..1....1...-7....0....1....0....0...-7....0....0....0....0....0....1....1....1
..1....0....5....1....0....0....1....0...-4....0....0...-4....1....0....0....1
..6....5...-2...-2...-3...-1....0....6....5...-2...-2....6...-4...-3...-2...-2
.-5...-2....0...-1....5...-1...-1...-4....1....6....2....4....3....3...-1....4
.-1...-4....1....7...-1....3...-2....3...-5....0....7...-4....1....4....6...-4
..3....3....1...-1....4...-5....4...-7....5....0...-3....0....2...-1...-2....7

Crossrefs

Cf. A221967.

Sequence in context: A207855 A207423 A207738 * A208080 A224264 A223921

Adjacent sequences: A221963 A221964 A221965 * A221967 A221968 A221969

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved