A250648 - OEIS

%I #6 May 24 2024 13:16:13

%S 20,125,476,1293,2954,5901,10766,18305,29478,45361,67364,96961,135976,

%T 186445,250688,331213,431054,553277,701474,879553,1091754,1342593,

%U 1637320,1981153,2380028,2840317,3368740,3972397,4659346,5437517,6315766

%N Number of length 4+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%C Row 4 of A250646.

%H R. H. Hardin, <a href="/A250648/b250648.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +2*a(n-2) +a(n-3) -4*a(n-4) -5*a(n-5) +3*a(n-6) +6*a(n-7) +3*a(n-8) -5*a(n-9) -4*a(n-10) +a(n-11) +2*a(n-12) +a(n-13) -a(n-14).

%F Empirical for n mod 6 = 0: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (124/45)*n + 1.

%F Empirical for n mod 6 = 1: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (151/27)*n^2 + (1361/405)*n + (301/162).

%F Empirical for n mod 6 = 2: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (1036/405)*n + (49/81).

%F Empirical for n mod 6 = 3: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (169/45)*n + (5/2).

%F Empirical for n mod 6 = 4: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (151/27)*n^2 + (956/405)*n + (29/81).

%F Empirical for n mod 6 = 5: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (1441/405)*n + (341/162).

%e Some solutions for n=6

%e ..0....0....3....2....1....2....3....0....0....1....1....1....5....0....1....4

%e ..2....5....6....2....4....6....2....6....4....6....3....3....6....6....6....0

%e ..5....1....6....0....1....5....4....1....3....0....0....3....5....4....5....2

%e ..2....2....6....5....6....5....3....6....4....5....6....4....5....6....5....1

%e ..2....1....5....1....5....1....3....4....1....2....2....1....0....4....3....4

%Y Cf. A250646.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014