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

1,1

Comments

Row 3 of A202962.

Links

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

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

Adjacent sequences: A202962 A202963 A202964 * A202966 A202967 A202968

Keyword

nonn

Author

R. H. Hardin, Dec 26 2011

Status

approved