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

1,1

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) = (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

Example

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

Crossrefs

Row 3 of A250167.

Sequence in context: A302619 A302411 A303178 * A244870 A309281 A296537

Adjacent sequences: A250165 A250166 A250167 * A250169 A250170 A250171

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved