%I #8 Nov 07 2018 10:03:24
%S 30,231,900,2701,6210,12931,23400,40281,63750,97951,142380,202981,
%T 278250,376251,494160,642481,816750,1030231,1276500,1571901,1907730,
%U 2303731,2748600,3265801,3841110,4502031,5231100,6060181,6968250,7991851,9106080
%N Number of length 1+4 0..n arrays with some pair in every consecutive five terms totalling exactly n.
%H R. H. Hardin, <a href="/A246893/b246893.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
%F Conjectures from _Colin Barker_, Nov 07 2018: (Start)
%F G.f.: x*(30 + 171*x + 378*x^2 + 619*x^3 + 394*x^4 + 329*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).
%F a(n) = 1 - 5*n + 30*n^2 - 5*n^3 + 10*n^4 for n even.
%F a(n) = -15 + 20*n + 20*n^2 - 5*n^3 + 10*n^4 for n odd.
%F (End)
%e Some solutions for n=6:
%e ..5....5....5....4....6....3....4....5....5....3....3....0....3....3....3....1
%e ..1....5....3....1....2....5....1....2....2....3....4....4....0....6....3....6
%e ..3....3....3....2....3....6....5....5....0....6....1....4....1....3....1....5
%e ..2....1....1....2....4....0....0....5....6....0....4....0....5....1....3....2
%e ..3....4....4....1....1....2....6....4....6....0....2....6....4....2....2....2
%Y Row 1 of A246892.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 06 2014