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A264417 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.

%I A264417 #5 Nov 12 2015 22:57:45
%S A264417 2,3,20,85,351,1462,6021,25188,104870,437164,1821829,7592125,31637827,
%T A264417 131836355,549380672,2289347792,9540065618,39754914509,165664757540,
%U A264417 690350003398,2876792156808,11988025615109,49955906989734
%N A264417 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.
%C A264417 Column 2 of A264422.
%H A264417 R. H. Hardin, <a href="/A264417/b264417.txt">Table of n, a(n) for n = 1..210</a>
%F A264417 Empirical: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +29*a(n-4) +13*a(n-5) +64*a(n-6) +161*a(n-7) -12*a(n-8) +82*a(n-9) -257*a(n-10) -1288*a(n-11) -1368*a(n-12) -2536*a(n-13) -3049*a(n-14) -516*a(n-15) -4280*a(n-16) -1979*a(n-17) +1117*a(n-18) +1724*a(n-19) +10832*a(n-20) +12414*a(n-21) -146*a(n-22) +13134*a(n-23) +10828*a(n-24) -6040*a(n-25) +4027*a(n-26) -4916*a(n-27) -23812*a(n-28) -5121*a(n-29) +3663*a(n-30) -6131*a(n-31) -1747*a(n-32) -1254*a(n-33) +1643*a(n-34) -722*a(n-35) -905*a(n-36) +386*a(n-37) +72*a(n-38) -695*a(n-39) -249*a(n-40) +334*a(n-41) +108*a(n-42) -44*a(n-43) +64*a(n-44) +149*a(n-45) -10*a(n-46) +36*a(n-47) +29*a(n-48) +46*a(n-49) -2*a(n-50) -8*a(n-51) +4*a(n-52) +5*a(n-53) +2*a(n-54) +a(n-55) +a(n-56)
%e A264417 Some solutions for n=4
%e A264417 ..4..5..1....4..5..1....4..5..3....4..5..3....4..5..1....4..5..1....4..8..1
%e A264417 ..0..8..2....0..8..2...10..1..2....0..1..2....7..8..2....0..8..2....0.11..2
%e A264417 ..3..6..7....3.11..7...13.14..0...10.11..7...10.11..0...10..6..7...10.14..5
%e A264417 .13.14.12....6.14.12....6..7..8...13.14..8....6.14..3...13.14..3....6..7..3
%e A264417 ..9.10.11....9.10.13....9.12.11....9.12..6....9.12.13....9.12.11....9.12.13
%Y A264417 Cf. A264422.
%K A264417 nonn
%O A264417 1,1
%A A264417 _R. H. Hardin_, Nov 12 2015