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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 20:03 EDT 2019. Contains 324380 sequences. (Running on oeis4.)