A202965 Number of arrays of 5 integers in -n..n with sum zero and adjacent elements differing in absolute value.

2, 82, 414, 1562, 4048, 9010, 17296, 30648, 50232, 78388, 116614, 167824, 233858, 318234, 423094, 552554, 709104, 897434, 1120360, 1383176, 1689016, 2043772, 2450910, 2916896, 3445538, 4043906, 4716110, 5469818, 6309488, 7243362, 8276224

Offset: 1

Author

R. H. Hardin, Dec 26 2011

Keywords

• nonn

Comments

Row 3 of A202962.

Examples

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

Links

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

Crossrefs

Cf. A202962.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11).

Empirical g.f.: 2*x*(1 + 39*x + 125*x^2 + 368*x^3 + 503*x^4 + 666*x^5 + 499*x^6 + 384*x^7 + 120*x^8 + 55*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jun 03 2018