A245953 - OEIS

%I #10 Nov 05 2018 18:09:16

%S 48,545,2304,7769,18384,39721,73728,130193,211440,332561,496128,

%T 723625,1017744,1407449,1895424,2519201,3281328,4228993,5364480,

%U 6745721,8374608,10320905,12585984,15252529,18321264,21888881,25955328,30632393,35919120

%N Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

%H R. H. Hardin, <a href="/A245953/b245953.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 05 2018: (Start)

%F G.f.: x*(48 + 401*x + 669*x^2 + 1241*x^3 - 851*x^4 - 557*x^5 + 7*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).

%F a(n) = 1 + 26*n - 17*n^2 + 24*n^3 + 21*n^4 + n^5 for n even.

%F a(n) = 39 - n - 36*n^2 + 24*n^3 + 21*n^4 + n^5 for n odd.

%F (End)

%e Some solutions for n=8:

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

%e ..1....3....7....8....8....0....1....1....6....2....8....8....6....3....4....5

%e ..2....4....2....5....7....8....5....4....8....4....0....4....1....6....2....3

%e ..6....5....8....3....1....4....7....7....3....5....6....5....5....5....6....8

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

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

%Y Row 3 of A245950.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 08 2014