login
A202965
Number of arrays of 5 integers in -n..n with sum zero and adjacent elements differing in absolute value.
1
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
1,1
COMMENTS
Row 3 of A202962.
LINKS
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
EXAMPLE
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
CROSSREFS
Cf. A202962.
Sequence in context: A120826 A343588 A259308 * A307583 A061994 A332584
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 26 2011
STATUS
approved