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A250362 Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 3 times.

%I A250362 #7 Nov 13 2018 08:38:08
%S A250362 16,81,255,623,1293,2397,4091,6555,9993,14633,20727,28551,38405,50613,
%T A250362 65523,83507,104961,130305,159983,194463,234237,279821,331755,390603,
%U A250362 456953,531417,614631,707255,809973,923493,1048547,1185891,1336305
%N A250362 Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 3 times.
%H A250362 R. H. Hardin, <a href="/A250362/b250362.txt">Table of n, a(n) for n = 1..210</a>
%F A250362 Empirical: a(n) = n^4 + 4*n^3 + 6*n^2 + 3*n + 3 for n>1.
%F A250362 Conjectures from _Colin Barker_, Nov 13 2018: (Start)
%F A250362 G.f.: x*(16 + x + 10*x^2 - 2*x^3 - 2*x^4 + x^5) / (1 - x)^5.
%F A250362 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A250362 (End)
%e A250362 Some solutions for n=6:
%e A250362 ..1....2....1....3....1....5....3....5....0....0....5....0....5....3....2....4
%e A250362 ..2....3....5....7....4....6....4....3....3....2....6....5....4....4....4....6
%e A250362 ..8....4....2....5....2....8....7....2....6....5....4....7....6....7....3....2
%e A250362 ..3....6....6....9....9....6....7....4....8....7....5....6....7....9....4....9
%Y A250362 Row 4 of A250361.
%K A250362 nonn
%O A250362 1,1
%A A250362 _R. H. Hardin_, Nov 19 2014