A253131 Number of length 3+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.

16, 90, 281, 673, 1356, 2452, 4083, 6409, 9584, 13806, 19261, 26185, 34796, 45368, 58151, 73457, 91568, 112834, 137569, 166161, 198956, 236380, 278811, 326713, 380496, 440662, 507653, 582009, 664204, 754816, 854351, 963425, 1082576, 1212458

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..121

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7).

Empirical for n mod 2 = 0: a(n) = (35/48)*n^4 + (47/8)*n^3 + (73/12)*n^2 + 3*n + 1.

Empirical for n mod 2 = 1: a(n) = (35/48)*n^4 + (47/8)*n^3 + (73/12)*n^2 + (21/8)*n + (11/16).

Empirical g.f.: x*(16 + 42*x + 27*x^2 - 12*x^4 - 4*x^5 + x^6) / ((1 - x)^5*(1 + x)^2). - Colin Barker, Dec 09 2018

Example

Some solutions for n=10:
.10....8....7....2....3....0....4...10....3....7....0....9....3....5....5...10
..0....1....3....9....3....4....1....4....1....0....1....1....0....0...10....6
..4...10....3....1....6....3....1....0....4....7....1....4....1....1....5....1
..8....0....7....1....0...10....5....8....0....0....2....9....0....2...10....5
..8....9....6....4....7....7....2....8....4...10....4....8....7....3....3....0

Crossrefs

Row 3 of A253129.

Sequence in context: A240262 A264531 A192129 * A119771 A055920 A055856

Adjacent sequences: A253128 A253129 A253130 * A253132 A253133 A253134

Keyword

nonn

Author

R. H. Hardin, Dec 27 2014

Status

approved