A200456 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero first and second differences.

4, 44, 142, 342, 678, 1148, 1832, 2744, 3874, 5334, 7114, 9192, 11708, 14644, 17962, 21826, 26206, 31044, 36544, 42660, 49310, 56734, 64866, 73616, 83256, 93696, 104834, 116970, 130006, 143824, 158748, 174668, 191446, 209446, 228542, 248572

Offset

1,1

Comments

Row 2 of A200454.

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) -2*a(n-4) +a(n-5) -2*a(n-6) +a(n-7) -2*a(n-8) +2*a(n-9) +a(n-11) -a(n-12).

Empirical g.f.: 2*(1 + x)*(2 + 18*x + 31*x^2 + 65*x^3 + 63*x^4 + 72*x^5 + 52*x^6 + 39*x^7 + 9*x^8 + 9*x^9) / ((1 - x)^4*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 21 2018

Example

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

Crossrefs

Cf. A200454.

Sequence in context: A344871 A071125 A193448 * A292454 A292734 A053314

Adjacent sequences: A200453 A200454 A200455 * A200457 A200458 A200459

Keyword

nonn

Author

R. H. Hardin, Nov 18 2011

Status

approved