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A268264 Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

%I A268264 #7 Jan 13 2019 08:49:17
%S A268264 33,273,1616,6877,22710,62249,148468,318261,627242,1155265,2012664,
%T A268264 3347213,5351806,8272857,12419420,18173029,25998258,36454001,50205472,
%U A268264 68036925,90865094,119753353,155926596,200786837,255929530,323160609
%N A268264 Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
%H A268264 R. H. Hardin, <a href="/A268264/b268264.txt">Table of n, a(n) for n = 1..210</a>
%F A268264 Empirical: a(n) = n^6 + n^5 + 5*n^4 + 4*n^3 + 12*n^2 + 6*n + 5 for n>1.
%F A268264 Conjectures from _Colin Barker_, Jan 13 2019: (Start)
%F A268264 G.f.: x*(33 + 42*x + 398*x^2 + 143*x^3 + 107*x^4 - 2*x^5 - 2*x^6 + x^7) / (1 - x)^7.
%F A268264 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.
%F A268264 (End)
%e A268264 Some solutions for n=7:
%e A268264 ..6....0....4....7....2....6....4....6....5....0....7....0....5....7....1....3
%e A268264 ..3....6....1....2....4....0....6....1....0....2....0....0....2....3....2....2
%e A268264 ..2....7....7....3....6....3....7....0....0....7....7....2....4....6....3....5
%e A268264 ..6....0....0....6....3....0....2....4....6....5....6....1....3....3....5....7
%e A268264 ..0....0....5....2....2....4....5....5....1....4....4....0....4....7....3....6
%e A268264 ..3....4....6....0....0....1....7....1....3....5....0....4....2....2....2....3
%Y A268264 Row 5 of A268261.
%K A268264 nonn
%O A268264 1,1
%A A268264 _R. H. Hardin_, Jan 29 2016