A264090 - OEIS

%I #6 Nov 10 2015 11:22:06

%S 4,9,8,25,39,16,64,245,169,32,169,1448,2401,715,64,441,8788,32761,

%T 24010,3025,128,1156,52941,456976,645627,240100,12815,256,3025,319906,

%U 6355441,19553300,12723489,2401000,54289,512,7921,1931215,88529281,563080476

%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 index change +-(.,.) 0,0 0,1 or 2,-2.

%C Table starts

%C ...4.....9.......25.........64...........169.............441...............1156

%C ...8....39......245.......1448..........8788...........52941.............319906

%C ..16...169.....2401......32761........456976.........6355441...........88529281

%C ..32...715....24010.....645627......19553300.......563080476........16552783250

%C ..64..3025...240100...12723489.....836655625.....49887902736......3094960562500

%C .128.12815..2401000..252076323...35960283125...4553473226652....607571415109250

%C .256.54289.24010000.4994107561.1545608400625.415614152704689.119272286997956401

%H R. H. Hardin, <a href="/A264090/b264090.txt">Table of n, a(n) for n = 1..198</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

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

%F k=3: a(n) = 10*a(n-1) for n>3

%F k=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4)

%F k=5: [order 14]

%F k=6: [order 25] for n>27

%F k=7: [order 25] for n>27

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

%F n=2: [order 8]

%F n=3: a(n) = 14*a(n-1) +14*a(n-2) -210*a(n-3) +210*a(n-5) -14*a(n-6) -14*a(n-7) +a(n-8)

%F n=4: [order 52]

%F n=5: [order 96]

%e Some solutions for n=3 k=4

%e ..0..1..2.11..3....1..0.10.11..4....0..1..2..4..3....1..0..3..2..4

%e ..6..5..7..9..8....5..7..6.16..9....5..6..8.16.17....5..6.15..8.17

%e .10.12..4.14.13....2..3.12.13.14...11.10.13.12.14...11.10.12.13.14

%e .15.16.17.19.18...15..8.18.17.19....7.15..9.19.18....7.16..9.19.18

%Y Column 1 is A000079(n+1).

%Y Row 1 is A007598(n+2).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 03 2015