A267474 - OEIS

%I #7 Feb 05 2018 09:36:32

%S 38,418,2490,10119,31880,83972,193852,404589,779938,1410134,2418406,

%T 3968211,6271188,9595832,14276888,20725465,29439870,41017162,56165426,

%U 75716767,100641024,132060204,171263636,219723845,279113146,351320958

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

%C Row 6 of A267471.

%H R. H. Hardin, <a href="/A267474/b267474.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1.

%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)

%F G.f.: x*(38 + 152*x + 362*x^2 + 137*x^3 + 37*x^4 - 7*x^5 + x^6) / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=7:

%e ..0....6....6....4....1....2....0....0....2....0....2....4....0....2....6....4

%e ..5....3....3....2....4....1....7....1....0....6....1....5....2....0....5....6

%e ..1....2....5....5....0....6....2....7....2....7....6....3....6....1....7....2

%e ..6....6....6....2....2....5....3....3....6....7....7....0....2....0....0....0

%e ..1....2....1....6....6....7....7....1....6....3....7....4....3....5....3....7

%e ..5....5....0....1....6....4....2....6....6....1....1....7....1....0....1....4

%Y Cf. A267471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2016