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A264166 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

%I A264166 #10 Feb 25 2018 08:41:25
%S A264166 1,4,8,16,33,69,145,300,624,1300,2705,5629,11713,24376,50728,105564,
%T A264166 219681,457161,951361,1979800,4120000,8573800,17842241,37130041,
%U A264166 77268321,160796844,334621288,696353256,1449124353,3015655309,6275635985
%N A264166 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.
%C A264166 Column 1 of A264172.
%H A264166 R. H. Hardin, <a href="/A264166/b264166.txt">Table of n, a(n) for n = 1..210</a>
%F A264166 Empirical: a(n) = a(n-1) + a(n-2) + 2*a(n-3) + a(n-4) + a(n-5) -a(n-6).
%F A264166 Empirical g.f.: x*(1 + x)*(1 + 2*x + x^2 + x^3 - x^4) / ((1 + x^2)*(1 - x - 2*x^2 - x^3 + x^4)). - _Colin Barker_, Feb 25 2018
%e A264166 Some solutions for n=4:
%e A264166 ..5..1....0..1....0..1....0..1....5..0....0..1....5..0....5..1....5..0....0..1
%e A264166 ..0..2....2..3....7..3....7..2....2..1....7..3....7..1....0..3....2..1....2..3
%e A264166 ..4..3....9..5....2..4....9..3....4..3....2..5....2..3....2..4....9..3....4..5
%e A264166 ..6..7....4..7....6..5....4..5....6..7....4..6....4..6....6..7....4..7....6..7
%e A264166 ..8..9....6..8....8..9....6..8....8..9....8..9....8..9....8..9....6..8....8..9
%Y A264166 Cf. A264172.
%K A264166 nonn
%O A264166 1,2
%A A264166 _R. H. Hardin_, Nov 06 2015