cp's OEIS Frontend

A245953 Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

%I A245953 #10 Nov 05 2018 18:09:16
%S A245953 48,545,2304,7769,18384,39721,73728,130193,211440,332561,496128,
%T A245953 723625,1017744,1407449,1895424,2519201,3281328,4228993,5364480,
%U A245953 6745721,8374608,10320905,12585984,15252529,18321264,21888881,25955328,30632393,35919120
%N A245953 Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
%H A245953 R. H. Hardin, <a href="/A245953/b245953.txt">Table of n, a(n) for n = 1..210</a>
%F A245953 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 A245953 Conjectures from _Colin Barker_, Nov 05 2018: (Start)
%F A245953 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 A245953 a(n) = 1 + 26*n - 17*n^2 + 24*n^3 + 21*n^4 + n^5 for n even.
%F A245953 a(n) = 39 - n - 36*n^2 + 24*n^3 + 21*n^4 + n^5 for n odd.
%F A245953 (End)
%e A245953 Some solutions for n=8:
%e A245953 ..3....4....6....3....2....2....5....0....0....3....1....3....2....6....5....1
%e A245953 ..1....3....7....8....8....0....1....1....6....2....8....8....6....3....4....5
%e A245953 ..2....4....2....5....7....8....5....4....8....4....0....4....1....6....2....3
%e A245953 ..6....5....8....3....1....4....7....7....3....5....6....5....5....5....6....8
%e A245953 ..3....1....6....1....8....6....1....6....5....4....6....4....2....2....6....0
%e A245953 ..2....7....2....2....1....0....4....2....2....1....2....8....6....1....0....8
%Y A245953 Row 3 of A245950.
%K A245953 nonn
%O A245953 1,1
%A A245953 _R. H. Hardin_, Aug 08 2014