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Number of length 1+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum.
1

%I #36 Nov 07 2018 11:29:42

%S 8,48,168,440,960,1848,3248,5328,8280,12320,17688,24648,33488,44520,

%T 58080,74528,94248,117648,145160,177240,214368,257048,305808,361200,

%U 423800,494208,573048,660968,758640,866760,986048,1117248,1261128

%N Number of length 1+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum.

%H R. H. Hardin, <a href="/A247727/b247727.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + 2*n^3 + 3*n^2 + 2*n.

%F Conjectures from _Colin Barker_, Nov 07 2018: (Start)

%F G.f.: 8*x*(1 + x + x^2) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=6:

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

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

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

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

%Y Row 1 of A247726.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 23 2014