A264163 - OEIS

%I #6 Nov 10 2015 12:05:44

%S 4,10,10,29,72,29,89,412,412,89,260,2927,5296,2927,260,772,19204,

%T 82167,82167,19204,772,2281,126688,1149961,2765728,1149961,126688,

%U 2281,6741,845296,16609233,86079818,86079818,16609233,845296,6741,19940,5596616

%N 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 0,2 1,0 -1,0 or 2,0.

%C Table starts

%C .....4........10...........29.............89..............260..............772

%C ....10........72..........412...........2927............19204...........126688

%C ....29.......412.........5296..........82167..........1149961.........16609233

%C ....89......2927........82167........2765728.........86079818.......2726236497

%C ...260.....19204......1149961.......86079818.......5865099776.....408612967960

%C ...772....126688.....16609233.....2726236497.....408612967960...62592982984064

%C ..2281....845296....239550224....86548482676...28536242142800.9610501585172009

%C ..6741...5596616...3438669140..2736421213693.1983317242018219

%C .19940..37146638..49526113317.86706789763033

%C .58954.246557278.712398787569

%H R. H. Hardin, <a href="/A264163/b264163.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) +2*a(n-3) +4*a(n-5) -a(n-8)

%F k=2: [order 84]

%e Some solutions for n=3 k=4

%e ..1..0..3..4..2....1..0..3..4..9....5..2..3..1..9....5..2..0..4..3

%e ..6..5..8..9..7...10..7..2..6.14....0..7..6.13..8....6..1..8.13.14

%e .11.10.17.12.19...15.16.11..8.13...15.16.17.14..4...11.16.17.12..9

%e .16.15.18.13.14....5.17.12.19.18...10.11.12.19.18...10.15..7.19.18

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 06 2015