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A245875 Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n. 1

%I

%S 68,1281,4624,13961,30900,63241,113024,193137,305860,470321,688848,

%T 987961,1369844,1869561,2488960,3272801,4222404,5393377,6786320,

%U 8468841,10440628,12782441,15492864,18666961,22302020,26508561,31282384,36750617

%N Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

%H R. H. Hardin, <a href="/A245875/b245875.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).

%F Conjectures from _Colin Barker_, Nov 04 2018: (Start)

%F G.f.: x*(68 + 1077*x + 781*x^2 + 633*x^3 - 1143*x^4 - 561*x^5 + 103*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).

%F a(n) = 1 + 22*n + 31*n^2 + 77*n^3 + 29*n^4 + n^5 for n even.

%F a(n) = -5 - 44*n + 10*n^2 + 77*n^3 + 29*n^4 + n^5 for n odd.

%F (End)

%e Some solutions for n=8:

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

%e ..6....4....1....8....8....4....6....6....7....8....8....2....7....7....8....7

%e ..2....4....7....0....7....7....2....5....1....1....0....6....1....1....8....1

%e ..2....8....4....6....1....1....3....3....4....7....2....2....3....1....0....0

%e ..6....0....4....2....6....7....5....8....4....6....6....3....5....7....6....8

%e ..5....3....4....6....2....1....5....0....5....1....3....5....3....3....2....8

%e ..2....5....7....3....1....3....3....8....4....7....5....5....5....5....5....0

%e ..6....4....1....2....6....5....4....0....3....4....7....3....3....5....3....5

%Y Row 6 of A245869.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 04 2014

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Last modified September 17 09:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)