A250168 Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

8, 37, 96, 211, 380, 639, 976, 1437, 2000, 2721, 3568, 4607, 5796, 7211, 8800, 10649, 12696, 15037, 17600, 20491, 23628, 27127, 30896, 35061, 39520, 44409, 49616, 55287, 61300, 67811, 74688, 82097, 89896, 98261, 107040, 116419, 126236, 136687, 147600

Offset: 1

Author

R. H. Hardin, Nov 13 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 3 of A250167.

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) = (29/12)*n^3 + (11/4)*n^2 + (17/6)*n + 1.

Empirical for n mod 2 = 1: a(n) = (29/12)*n^3 + (11/4)*n^2 + (19/12)*n + (5/4).

Empirical g.f.: x*(8 + 21*x + 14*x^2 + 14*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 12 2018