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A264365 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

%I A264365 #8 Jan 07 2019 12:40:43
%S A264365 1,3,9,18,36,78,169,364,784,1680,3600,7740,16641,35733,76729,164815,
%T A264365 354025,760410,1633284,3508110,7535025,16184520,34762816,74666944,
%U A264365 160376896,344473464,739894401,1589218425,3413480625,7331811675
%N A264365 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
%H A264365 R. H. Hardin, <a href="/A264365/b264365.txt">Table of n, a(n) for n = 1..210</a>
%F A264365 Empirical: a(n) = a(n-1) + 3*a(n-3) + 3*a(n-4) + 3*a(n-5) + 3*a(n-6) - 2*a(n-8) - a(n-9).
%F A264365 Empirical g.f.: x*(1 + 2*x + 6*x^2 + 6*x^3 + 6*x^4 + 3*x^5 - 2*x^6 - 3*x^7 - x^8) / ((1 + x^2 - x^3)*(1 + x^2 + x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Jan 07 2019
%e A264365 Some solutions for n=4:
%e A264365 ..7..8..0..3..4....0..1..2..3..4....0..8..9..3..4....0..8..2..3..4
%e A264365 ..5..1..2..6..9....5..6..7..8..9....5..1..2..6..7....5..1..7..6..9
%Y A264365 Row 1 of A264364.
%K A264365 nonn
%O A264365 1,2
%A A264365 _R. H. Hardin_, Nov 12 2015