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%I #9 Nov 10 2015 12:25:47
%S 1,4,18,70,292,1212,5028,20832,86360,358008,1484112,6152272,25503888,
%T 105724928,438276640,1816850528,7531649344,31222019264,129429085248,
%U 536540828672,2224199146368,9220289638272,38222180397312,158447850514688
%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 1 or 2, and rows and columns in increasing lexicographic order.
%C Column 1 of A263586.
%H R. H. Hardin, <a href="/A263582/b263582.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +2*a(n-3) +4*a(n-4) -8*a(n-5).
%F Empirical: G.f.: -x*(-1-2*x^2+4*x^3) / ( 1-4*x-2*x^3-4*x^4+8*x^5 ). - _R. J. Mathar_, Nov 03 2015
%e Some solutions for n=4
%e ..1..2....1..2....1..2....2..3....1..2....1..3....1..2....1..5....2..3....2..3
%e ..3..0....5..0....3..0....5..0....3..0....4..0....4..0....4..0....4..0....4..0
%e ..5..4....6..3....5..6....6..1....7..6....7..2....7..6....6..2....7..1....6..1
%e ..7..8....8..4....8..4....7..4....8..4....8..5....8..3....8..3....8..5....7..8
%e ..9..6....9..7....9..7....9..8....9..5....9..6....9..5....9..7....9..6....9..5
%Y Cf. A263586.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 22 2015
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