A249983 Number of length 3+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 3*n.

20, 88, 208, 426, 728, 1178, 1744, 2508, 3420, 4580, 5920, 7558, 9408, 11606, 14048, 16888, 20004, 23568, 27440, 31810, 36520, 41778, 47408, 53636, 60268, 67548, 75264, 83678, 92560, 102190, 112320, 123248, 134708, 147016, 159888, 173658, 188024

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

Empirical for n mod 2 = 0: a(n) = (41/12)*n^3 + (43/4)*n^2 + (53/6)*n.

Empirical for n mod 2 = 1: a(n) = (41/12)*n^3 + (43/4)*n^2 + (79/12)*n - (3/4).

Empirical g.f.: 2*x*(10 + 24*x + 6*x^2 + x^3) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 10 2018

Example

Some solutions for n=6:
..9...11....5...12....2....4....5...11....4....7....0....0...11....8...12....4
..1....1...11....4....0...11....0...10....2....0....8....1....1...12....4...12
..2....4....2...10...10....6...10....2...10....1...10...10....0....0....3....7
.11....9....5....6....4....0....7...11....2...11....2....2....7....2...12...12

Crossrefs

Row 3 of A249982.

Sequence in context: A219824 A339343 A306987 * A234258 A213839 A264302

Adjacent sequences: A249980 A249981 A249982 * A249984 A249985 A249986

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved