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A264878 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 0,1 0,-1 -2,0 or 1,1.

%I A264878 #4 Nov 27 2015 07:34:35
%S A264878 1,0,1,1,0,1,0,1,0,2,1,1,5,0,3,0,7,4,20,0,4,1,20,65,12,56,0,5,0,49,
%T A264878 228,572,36,137,0,6,1,175,1101,2348,3613,108,295,0,8,0,323,4832,22152,
%U A264878 22400,19372,324,709,0,11,1,1085,18501,129230,356692,207424,103585,972,1983,0
%N A264878 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 0,1 0,-1 -2,0 or 1,1.
%C A264878 Table starts
%C A264878 ..1.0....1....0........1..........0............1..............0
%C A264878 ..1.0....1....1........7.........20...........49............175
%C A264878 ..1.0....5....4.......65........228.........1101...........4832
%C A264878 ..2.0...20...12......572.......2348........22152.........129230
%C A264878 ..3.0...56...36.....3613......22400.......356692........3303808
%C A264878 ..4.0..137..108....19372.....207424......4747695.......78535556
%C A264878 ..5.0..295..324...103585....1946752.....68488297.....1924357508
%C A264878 ..6.0..709..972...629654...18265856...1050281271....47123513432
%C A264878 ..8.0.1983.2916..3930725..171168256..16268725036..1152731721920
%C A264878 .11.0.5280.8748.23940621.1602206720.247512489984.28078658475952
%H A264878 R. H. Hardin, <a href="/A264878/b264878.txt">Table of n, a(n) for n = 1..179</a>
%F A264878 Empirical for column k:
%F A264878 k=1: a(n) = a(n-1) +a(n-5)
%F A264878 k=2: a(n) = a(n-1)
%F A264878 k=3: [order 45]
%F A264878 k=4: a(n) = 3*a(n-1) for n>3
%F A264878 Empirical for row n:
%F A264878 n=1: a(n) = a(n-2)
%F A264878 n=2: [order 20]
%F A264878 n=3: [order 46]
%e A264878 Some solutions for n=4 k=4
%e A264878 ..1..2..3..4.14...10..2.12..4.14....1..2.12..4.14...10..2..3..4.14
%e A264878 .15..0..8..9.19....6..0..1..9..3...15..0..8..9..3....6..0..1..9.19
%e A264878 .20..5..6..7.24...20..5.22..7..8...20..5..6..7.24...20..5.22..7..8
%e A264878 .16.10.11.12.13...16.17.11.19.13...16.10.11.19.13...16.17.11.12.13
%e A264878 .21.22.23.17.18...21.15.23.24.18...21.22.23.17.18...21.15.23.24.18
%Y A264878 Column 1 is A003520(n+1).
%Y A264878 Column 4 is A003946(n-2).
%K A264878 nonn,tabl
%O A264878 1,10
%A A264878 _R. H. Hardin_, Nov 27 2015