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A264676 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

%I A264676 #4 Nov 20 2015 19:52:19
%S A264676 0,1,1,1,2,0,1,10,9,0,1,29,34,19,1,3,75,123,145,44,0,3,201,748,890,
%T A264676 603,108,0,4,588,3698,9205,6851,2417,264,1,6,1700,17443,88687,123222,
%U A264676 43131,9976,649,0,9,4785,84737,714235,2025372,1449467,291315,40825,1573,0,12
%N A264676 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.
%C A264676 Table starts
%C A264676 .0....1......1........1...........1.............3..............3
%C A264676 .1....2.....10.......29..........75...........201............588
%C A264676 .0....9.....34......123.........748..........3698..........17443
%C A264676 .0...19....145......890........9205.........88687.........714235
%C A264676 .1...44....603.....6851......123222.......2025372.......29875350
%C A264676 .0..108...2417....43131.....1449467......43095017.....1095840260
%C A264676 .0..264...9976...291315....17406354.....918298857....40765995197
%C A264676 .1..649..40825..1980287...209749118...19297801298..1494347569074
%C A264676 .0.1573.166985.13199209..2503676777..404856272120.54204721906375
%C A264676 .0.3837.684253.88670692.29934965340.8489260394876
%H A264676 R. H. Hardin, <a href="/A264676/b264676.txt">Table of n, a(n) for n = 1..127</a>
%F A264676 Empirical for column k:
%F A264676 k=1: a(n) = a(n-3)
%F A264676 k=2: a(n) = 2*a(n-1) +a(n-3) +3*a(n-4) +2*a(n-5) -a(n-6) +4*a(n-7) -a(n-8) -a(n-10)
%F A264676 k=3: [order 15]
%F A264676 k=4: [order 26] for n>27
%F A264676 Empirical for row n:
%F A264676 n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)
%F A264676 n=2: [order 9]
%F A264676 n=3: [order 70]
%F A264676 n=4: [order 81] for n>86
%e A264676 Some solutions for n=4 k=4
%e A264676 ..6..8..1..2..3....7..8..1..2..3...12..8..1..2..3...12.13..1..2..3
%e A264676 ..0..5.14..7..4....0.13..6.14..4....0..5..6..7..4....0.18.19..7..4
%e A264676 .16.10.24.19..9....5.23.24.12..9...17.18.24.19..9....5..6.24..8..9
%e A264676 .21.11.12.13.18...10.11.16.17.18...10.11.16.13.14...10.11.16.17.14
%e A264676 .15.20.17.22.23...15.20.21.22.19...15.20.21.22.23...15.20.21.22.23
%Y A264676 Row 1 is A080013(n+1).
%K A264676 nonn,tabl
%O A264676 1,5
%A A264676 _R. H. Hardin_, Nov 20 2015