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A267474 Number of length-6 0..n arrays with no following elements larger than the first repeated value.

%I A267474 #7 Feb 05 2018 09:36:32
%S A267474 38,418,2490,10119,31880,83972,193852,404589,779938,1410134,2418406,
%T A267474 3968211,6271188,9595832,14276888,20725465,29439870,41017162,56165426,
%U A267474 75716767,100641024,132060204,171263636,219723845,279113146,351320958
%N A267474 Number of length-6 0..n arrays with no following elements larger than the first repeated value.
%C A267474 Row 6 of A267471.
%H A267474 R. H. Hardin, <a href="/A267474/b267474.txt">Table of n, a(n) for n = 1..210</a>
%F A267474 Empirical: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1.
%F A267474 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267474 G.f.: x*(38 + 152*x + 362*x^2 + 137*x^3 + 37*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A267474 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>7.
%F A267474 (End)
%e A267474 Some solutions for n=7:
%e A267474 ..0....6....6....4....1....2....0....0....2....0....2....4....0....2....6....4
%e A267474 ..5....3....3....2....4....1....7....1....0....6....1....5....2....0....5....6
%e A267474 ..1....2....5....5....0....6....2....7....2....7....6....3....6....1....7....2
%e A267474 ..6....6....6....2....2....5....3....3....6....7....7....0....2....0....0....0
%e A267474 ..1....2....1....6....6....7....7....1....6....3....7....4....3....5....3....7
%e A267474 ..5....5....0....1....6....4....2....6....6....1....1....7....1....0....1....4
%Y A267474 Cf. A267471.
%K A267474 nonn
%O A267474 1,1
%A A267474 _R. H. Hardin_, Jan 15 2016