A202964 Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.

4, 28, 108, 268, 544, 972, 1576, 2392, 3456, 4792, 6436, 8424, 10780, 13540, 16740, 20404, 24568, 29268, 34528, 40384, 46872, 54016, 61852, 70416, 79732, 89836, 100764, 112540, 125200, 138780, 153304, 168808, 185328, 202888, 221524, 241272

Offset

1,1

Comments

Row 2 of A202962.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6).

Empirical g.f.: 4*x*(1 + 4*x + 9*x^2 + 5*x^3 + 5*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Jun 03 2018

Example

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

Crossrefs

Cf. A202962.

Sequence in context: A077595 A201243 A092712 * A352322 A183469 A058227

Adjacent sequences: A202961 A202962 A202963 * A202965 A202966 A202967

Keyword

nonn

Author

R. H. Hardin, Dec 26 2011

Status

approved