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A246482 Number of length 3+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

%I A246482 #7 Nov 06 2018 06:45:05
%S A246482 2,20,292,1376,6534,20004,57416,133664,293770,574100,1073772,1865280,
%T A246482 3134222,5007716,7797904,11708864,17227026,24659604,34722740,47856800,
%U A246482 65070742,86971940,114932952,149765856,193285274,246549524,311901436
%N A246482 Number of length 3+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.
%H A246482 R. H. Hardin, <a href="/A246482/b246482.txt">Table of n, a(n) for n = 1..210</a>
%F A246482 Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).
%F A246482 Conjectures from _Colin Barker_, Nov 06 2018: (Start)
%F A246482 G.f.: 2*x*(1 + 7*x + 115*x^2 + 251*x^3 + 1161*x^4 + 1045*x^5 + 2001*x^6 + 617*x^7 + 562*x^8) / ((1 - x)^7*(1 + x)^4).
%F A246482 a(n) = -20*n + 43*n^2 - 40*n^3 + 21*n^4 - 6*n^5 + n^6 for n even.
%F A246482 a(n) = -26 + 37*n + 5*n^2 - 30*n^3 + 21*n^4 - 6*n^5 + n^6 for n odd.
%F A246482 (End)
%e A246482 Some solutions for n=6:
%e A246482 ..3....6....2....5....5....3....1....6....6....4....2....6....1....1....1....5
%e A246482 ..4....4....2....3....5....5....0....1....4....4....1....2....2....2....6....2
%e A246482 ..1....5....2....5....3....5....3....3....6....4....6....5....0....6....2....6
%e A246482 ..0....3....2....6....2....6....4....1....3....4....6....2....3....2....3....5
%e A246482 ..3....0....2....6....2....4....0....2....4....4....6....6....2....1....5....5
%e A246482 ..2....5....6....5....1....3....0....2....6....1....3....6....1....3....0....6
%Y A246482 Row 3 of A246479.
%K A246482 nonn
%O A246482 1,1
%A A246482 _R. H. Hardin_, Aug 27 2014