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A250168
Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved