A246480 - OEIS

%I #7 Nov 06 2018 06:44:52

%S 2,10,60,172,462,966,1880,3256,5370,8290,12372,17700,24710,33502,

%T 44592,58096,74610,94266,117740,145180,177342,214390,257160,305832,

%U 361322,423826,494340,573076,661110,758670,866912,986080,1117410,1261162

%N Number of length 1+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

%H R. H. Hardin, <a href="/A246480/b246480.txt">Table of n, a(n) for n = 1..210</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 Conjectures from _Colin Barker_, Nov 06 2018: (Start)

%F G.f.: 2*x*(1 + 2*x + 16*x^2 + 6*x^3 + 23*x^4) / ((1 - x)^5*(1 + x)^2).

%F a(n) = -n + 3*n^2 - 2*n^3 + n^4 for n even.

%F a(n) = -3 + 3*n + 3*n^2 - 2*n^3 + n^4 for n odd.

%F (End)

%e Some solutions for n=6:

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

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

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

%e ..2....4....2....4....5....5....4....5....5....5....0....2....0....4....5....5

%Y Row 1 of A246479.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 27 2014