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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)