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A221526 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more. 1

%I

%S 0,10,274,2172,9982,33380,90684,212812,447962,867012,1569640,2691164,

%T 4410102,6956452,10620692,15763500,22826194,32341892,44947392,

%U 61395772,82569710,109495524,143357932,185515532,237517002,301118020,378298904

%N Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more.

%C Row 6 of A221524.

%H R. H. Hardin, <a href="/A221526/b221526.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1*n^6 - 20*n^4 + 83*n^3 - 182*n^2 + 236*n - 148 for n>3.

%F Conjectures from _Colin Barker_, Aug 06 2018: (Start)

%F G.f.: 2*x^2*(5 + 102*x + 232*x^2 + 91*x^3 - 61*x^4 + 3*x^5 - 15*x^6 + 4*x^7 - x^8) / (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>10.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A221524.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013

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Last modified May 28 13:05 EDT 2022. Contains 354115 sequences. (Running on oeis4.)