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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)