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A264550 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 -1,2 1,0 or 0,-1.

%I A264550 #4 Nov 17 2015 15:37:08
%S A264550 0,1,1,1,2,0,1,6,5,0,1,16,16,10,1,3,40,36,45,21,0,3,96,172,216,133,44,
%T A264550 0,4,240,764,1528,1160,400,93,1,6,608,2728,11728,14852,4640,1204,196,
%U A264550 0,9,1536,9880,66372,163744,105081,23140,3561,413,0,12,3840,38818,403920
%N A264550 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 -1,2 1,0 or 0,-1.
%C A264550 Table starts
%C A264550 .0...1.....1.......1.........1...........3.............3...............4
%C A264550 .1...2.....6......16........40..........96...........240.............608
%C A264550 .0...5....16......36.......172.........764..........2728............9880
%C A264550 .0..10....45.....216......1528.......11728.........66372..........403920
%C A264550 .1..21...133....1160.....14852......163744.......1573479........16103502
%C A264550 .0..44...400....4640....105081.....1994830......29691127.......480994368
%C A264550 .0..93..1204...23140....813473....25172836.....591482528.....15554895920
%C A264550 .1.196..3561..110592...6587227...316806958...11959837149....510948245264
%C A264550 .0.413.10554..501828..50597392..3939510885..234588752099..16034698666868
%C A264550 .0.870.31493.2390752.392445418.49105816488.4630258704238.508458281055496
%H A264550 R. H. Hardin, <a href="/A264550/b264550.txt">Table of n, a(n) for n = 1..198</a>
%F A264550 Empirical for column k:
%F A264550 k=1: a(n) = a(n-3)
%F A264550 k=2: a(n) = 2*a(n-1) +a(n-4)
%F A264550 k=3: [order 15]
%F A264550 k=4: [order 10] for n>11
%F A264550 k=5: [order 84]
%F A264550 Empirical for row n:
%F A264550 n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)
%F A264550 n=2: a(n) = 2*a(n-1) +8*a(n-4)
%F A264550 n=3: [order 70]
%F A264550 n=4: [order 56] for n>59
%e A264550 Some solutions for n=4 k=4
%e A264550 ..1..2..5..6..7....1..2..3..4..7....1..2..3..7..8....1..5..3..6..8
%e A264550 ..0.10..8..3..4....0.10..8.11.12....0.10.11.12..4....0..7..2.12..4
%e A264550 .11.12.15.14..9....5..6.13.17..9....5..6.13.17..9...11.15.13.14..9
%e A264550 .16.20.18.13.23...16.20.18.21.14...16.20.18.21.14...10.20.18.22.23
%e A264550 .21.22.17.24.19...15.22.23.24.19...15.22.23.24.19...21.16.17.24.19
%Y A264550 Row 1 is A080013(n+1).
%K A264550 nonn,tabl
%O A264550 1,5
%A A264550 _R. H. Hardin_, Nov 17 2015