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Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 0 or 2, and rows and columns in increasing lexicographic order.
1

%I #11 Jan 02 2019 07:24:12

%S 2,8,24,60,160,448,1232,3344,9120,24960,68224,186304,508928,1390592,

%T 3799296,10379520,28357120,77473792,211662848,578272256,1579868160,

%U 4316282880,11792306176,32217174016,88018952192,240472260608

%N Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 0 or 2, and rows and columns in increasing lexicographic order.

%H R. H. Hardin, <a href="/A263598/b263598.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-3) + 4*a(n-4).

%F Empirical g.f.: 2*x*(1 + 2*x + 4*x^2 + 2*x^3) / ((1 + 2*x^2)*(1 - 2*x - 2*x^2)). - _Colin Barker_, Jan 02 2019

%e Some solutions for n=4:

%e ..0..2....0..2....0..2....0..2....0..1....0..1....0..2....0..2....0..5....0..1

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

%e ..3..5....4..6....4..5....3..5....3..6....4..5....3..9....3..9....4..1....3..9

%e ..6..4....5..7....6..7....6..7....5..8....6..7....6..4....5..8....6..7....5..4

%e ..8..9....8..9....8..9....8..9....7..9....8..9....8..5....7..6....8..9....8..6

%Y Column 1 of A263602.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 22 2015