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 A221598 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less. 1

%I

%S 64,393,1210,2715,5082,8475,13056,18987,26430,35547,46500,59451,74562,

%T 91995,111912,134475,159846,188187,219660,254427,292650,334491,380112,

%U 429675,483342,541275,603636,670587,742290,818907,900600,987531,1079862

%N Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less.

%C Row 6 of A221596.

%H R. H. Hardin, <a href="/A221598/b221598.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3.

%F Conjectures from _Colin Barker_, Aug 09 2018: (Start)

%F G.f.: x*(64 + 137*x + 22*x^2 - 23*x^3 - 26*x^4 - 10*x^5 - 2*x^6) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A221596.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2013

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Last modified March 21 16:33 EDT 2023. Contains 361408 sequences. (Running on oeis4.)