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A264623 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

%I A264623 #4 Nov 19 2015 06:51:33
%S A264623 0,4,13,22,61,280,832,2373,7225,24371,74664,229729,715055,2264780,
%T A264623 7040309,21916773,68434305,214187227,668160424,2084764226,6510150515,
%U A264623 20333712284,63475055481,198151996889,618702544012,1931805153845
%N A264623 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.
%C A264623 Column 3 of A264628.
%H A264623 R. H. Hardin, <a href="/A264623/b264623.txt">Table of n, a(n) for n = 1..210</a>
%F A264623 Empirical: a(n) = 6*a(n-2) +10*a(n-3) +33*a(n-4) -5*a(n-5) -175*a(n-6) -235*a(n-7) -281*a(n-8) +137*a(n-9) +1360*a(n-10) +1709*a(n-11) +923*a(n-12) -602*a(n-13) -3180*a(n-14) -4831*a(n-15) -3269*a(n-16) +499*a(n-17) +3130*a(n-18) +4030*a(n-19) +4286*a(n-20) +2250*a(n-21) -653*a(n-22) -816*a(n-23) -617*a(n-24) -1339*a(n-25) -1262*a(n-26) -109*a(n-27) +234*a(n-28) -419*a(n-29) -307*a(n-30) +265*a(n-31) +234*a(n-32) +80*a(n-33) -114*a(n-34) +69*a(n-35) +143*a(n-36) -99*a(n-37) -22*a(n-38) +28*a(n-39) +11*a(n-40) -9*a(n-41) -14*a(n-42) +15*a(n-43) -6*a(n-44) +a(n-45)
%e A264623 Some solutions for n=4
%e A264623 ..1..9..3..7....4..2..3..7....1..2..3..7....1..2..3.11....1..2..3.11
%e A264623 ..5..0.10..2...12..0..1.11....5..0.10.15...12..0..7.15....5..0..7.15
%e A264623 .12..4.11..6....9.10..5..6....9..4.11..6...16..4..5..6...16..4.18..6
%e A264623 .16..8.15.19...16..8.15.19...16..8.18.19...13..8..9.10...13..8..9.10
%e A264623 .17.18.13.14...17.18.13.14...17.12.13.14...17.18.19.14...17.12.19.14
%Y A264623 Cf. A264628.
%K A264623 nonn
%O A264623 1,2
%A A264623 _R. H. Hardin_, Nov 19 2015