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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

%I #7 Dec 09 2018 06:43:26

%S 16,90,281,673,1356,2452,4083,6409,9584,13806,19261,26185,34796,45368,

%T 58151,73457,91568,112834,137569,166161,198956,236380,278811,326713,

%U 380496,440662,507653,582009,664204,754816,854351,963425,1082576,1212458

%N 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.

%H R. H. Hardin, <a href="/A253131/b253131.txt">Table of n, a(n) for n = 1..121</a>

%F 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).

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

%F 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).

%F 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

%e Some solutions for n=10:

%e .10....8....7....2....3....0....4...10....3....7....0....9....3....5....5...10

%e ..0....1....3....9....3....4....1....4....1....0....1....1....0....0...10....6

%e ..4...10....3....1....6....3....1....0....4....7....1....4....1....1....5....1

%e ..8....0....7....1....0...10....5....8....0....0....2....9....0....2...10....5

%e ..8....9....6....4....7....7....2....8....4...10....4....8....7....3....3....0

%Y Row 3 of A253129.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 27 2014

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