A193643 Number of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero

1, 7, 19, 67, 217, 721, 2377, 7855, 25939, 85675, 282961, 934561, 3086641, 10194487, 33670099, 111204787, 367284457, 1213058161, 4006458937, 13232434975, 43703763859, 144343726555, 476734943521, 1574548557121, 5200380614881

Offset

1,2

Comments

Column 3 of A193648

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

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

Empirical: G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x^2+3*x-1) ). - R. J. Mathar, Feb 19 2015

Empirical: a(n)+a(n+1) = 2*A003688(n+1). - R. J. Mathar, Feb 19 2015

Example

Some solutions for n=6
..2....1...-1....0....0....0....1....0....2...-2....2....1...-3....0....0....0
.-2...-1....1...-1...-3....0...-1....3...-2....2...-2...-1....3...-2....0....0
.-1....1....2....1....3....0....1...-3....2...-3...-2...-3....1....2....2....0
..1....0...-2...-3...-1...-2....1....3....0....3....2....3...-1....0...-2...-3
.-1...-3....0....3....1....2...-1...-3...-2....0....1...-2....2....2....2....3
..0....3....0...-3....0....0....1....0....2....0...-1....2...-2...-2...-2....0

Crossrefs

Sequence in context: A155218 A305483 A046137 * A228026 A122484 A155242

Adjacent sequences: A193640 A193641 A193642 * A193644 A193645 A193646

Keyword

nonn

Author

R. H. Hardin Aug 02 2011

Status

approved