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%I #7 Nov 06 2018 12:08:26
%S 2,16,260,1096,5430,15960,47432,109552,246890,483520,920652,1606776,
%T 2735390,4392136,6907280,10419040,15447762,22202352,31455380,43507240,
%U 59453702,79710136,105775320,138205776,178991930,228860320,290390492
%N Number of length 2+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.
%H R. H. Hardin, <a href="/A246739/b246739.txt">Table of n, a(n) for n = 1..210</a>
%F 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 Conjectures from _Colin Barker_, Nov 06 2018: (Start)
%F G.f.: 2*x*(1 + 5*x + 105*x^2 + 161*x^3 + 1023*x^4 + 655*x^5 + 2211*x^6 + 523*x^7 + 1076*x^8) / ((1 - x)^7*(1 + x)^4).
%F a(n) = -58*n + 111*n^2 - 87*n^3 + 36*n^4 - 8*n^5 + n^6 for n even.
%F a(n) = -70 + 80*n + 34*n^2 - 71*n^3 + 36*n^4 - 8*n^5 + n^6 for n odd.
%F (End)
%e Some solutions for n=4:
%e ..4....1....4....2....4....2....1....4....0....2....1....2....0....4....2....2
%e ..4....0....3....0....4....1....1....2....1....1....1....0....2....1....1....3
%e ..3....2....3....0....4....0....1....4....1....1....0....1....1....4....0....3
%e ..2....0....3....3....4....0....1....3....2....1....2....0....1....4....0....3
%e ..3....0....3....0....2....0....1....3....1....4....0....1....1....4....0....4
%e ..3....3....2....2....1....1....4....3....0....4....1....2....1....2....0....2
%Y Row 2 of A246737.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 02 2014
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