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%I #10 Mar 20 2018 20:37:10
%S 4,18,81,288,1024,3872,14641,54450,202500,756450,2825761,10543232,
%T 39337984,146821248,547981281,2045057058,7632119044,28483593842,
%U 106302733681,396726688800,1480602240000,5525684704800,20622143227921
%N Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having index change (+-,+-) 0,0 1,2 or 1,0.
%C Row 1 of A264003.
%H R. H. Hardin, <a href="/A264004/b264004.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 12*a(n-3) - 12*a(n-5) + 4*a(n-6) - 4*a(n-7) + a(n-8).
%F Empirical g.f.: x*(4 + 2*x + 25*x^2 - 12*x^3 - 20*x^4 + 4*x^5 - 7*x^6 + 2*x^7) / ((1 - x)*(1 + x)*(1 - 4*x + x^2)*(1 + 4*x^2 + x^4)). - _Colin Barker_, Mar 20 2018
%e Some solutions for n=4:
%e ..0..1..7..3..9....0..8..7..6..4....0..6..9..8..7....0..6..9..8..7
%e ..5..6..4..8..2....5..3..2..1..9....5..3..2..1..4....5..1..4..3..2
%Y Cf. A264003.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 31 2015
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