A250647 Number of length 3+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

6, 23, 44, 89, 134, 219, 296, 433, 550, 751, 916, 1193, 1414, 1779, 2064, 2529, 2886, 3463, 3900, 4601, 5126, 5963, 6584, 7569, 8294, 9439, 10276, 11593, 12550, 14051, 15136, 16833, 18054, 19959, 21324, 23449, 24966, 27323, 29000, 31601, 33446, 36303

Offset

1,1

Links

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

Formula

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

Empirical for n mod 2 = 0: a(n) = (5/12)*n^3 + 3*n^2 + (10/3)*n + 1.

Empirical for n mod 2 = 1: a(n) = (5/12)*n^3 + (11/4)*n^2 + (31/12)*n + (1/4).

Empirical g.f.: x*(6 + 17*x + 3*x^2 - 6*x^3 + x^5 - x^6) / ((1 - x)^4*(1 + x)^3). - Colin Barker, Nov 15 2018

Example

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

Crossrefs

Row 3 of A250646.

Sequence in context: A161446 A081097 A031293 * A304392 A235332 A026817

Adjacent sequences: A250644 A250645 A250646 * A250648 A250649 A250650

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved