A200182 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).

3, 6, 11, 14, 19, 26, 31, 38, 47, 54, 63, 74, 83, 94, 107, 118, 131, 146, 159, 174, 191, 206, 223, 242, 259, 278, 299, 318, 339, 362, 383, 406, 431, 454, 479, 506, 531, 558, 587, 614, 643, 674, 703, 734, 767, 798, 831, 866, 899, 934, 971, 1006, 1043, 1082, 1119, 1158

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5)

a(3*k-2) = ((3*k+1)^2)/3 - 7/3.

a(3*k-1) = ((3*k+2)^2)/3 - 7/3.

a(3*k) = ((3*k+3)^2)/3 - 1 = 3*(k+1)^2 - 1.

a(3*k+1) = ((3*k+4)^2)/3 - 7/3.

a(3*k+2) = ((3*k+5)^2)/3 - 7/3 ... and so on.

The terms a(3*k-1) and a(3*k+1) seem to be terms of A241199: numbers n such that 4 consecutive terms of binomial(n,k) satisfy a quadratic relation for 0 <= k <= n/2. - Avi Friedlich, Apr 28 2015

Empirical g.f.: -x*(2*x^4-5*x^3+2*x^2+3) / ((x-1)^3*(x^2+x+1)). - Colin Barker, Apr 28 2015

Example

Some solutions for n=6:
..3....4....2....6....5....2....0....6....1....0....0....5....6....1....4....3
.-2....0....1...-2....6....3...-1...-1....2....1....1....0...-3....0...-1....1
.-1....1....2...-1...-6...-3....0....0....3....2...-1....1...-2....1....0....2
..0...-5...-5...-3...-5...-2....1...-5...-6...-3....0...-6...-1...-2...-3...-6

Crossrefs

Row 4 of A200181.

A014206 is a related sequence.

Sequence in context: A047398 A047924 A267519 * A342173 A282277 A122599

Adjacent sequences: A200179 A200180 A200181 * A200183 A200184 A200185

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved