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

Author

R. H. Hardin, Nov 26 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 3 of A250646.

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