login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264569 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 1,0 1,1 0,-1 or -1,1. 13

%I

%S 1,1,1,1,2,1,2,4,4,2,2,8,10,8,2,4,24,44,31,16,3,4,64,143,192,79,32,4,

%T 7,160,633,1130,888,224,64,5,9,384,2172,8356,7808,4104,646,128,7,13,

%U 960,8409,47571,96429,57265,18540,1784,256,9,18,2432,32046,305844,868613

%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 1,0 1,1 0,-1 or -1,1.

%C Table starts

%C .1...1.....1.......2.........2...........4.............4...............7

%C .1...2.....4.......8........24..........64...........160.............384

%C .1...4....10......44.......143.........633..........2172............8409

%C .2...8....31.....192......1130........8356.........47571..........305844

%C .2..16....79.....888......7808.......96429........868613.........8968735

%C .3..32...224....4104.....57265.....1133040......16284544.......273793368

%C .4..64...646...18540....403872....13182464.....298587595......8004883334

%C .5.128..1784...85752...2873739...152082304....5442431797....235814997396

%C .7.256..5010..389340..20432891..1755041376...99386232806...6882481295560

%C .9.512.14026.1787832.144677017.20212718576.1803702025944.200087118615516

%H R. H. Hardin, <a href="/A264569/b264569.txt">Table of n, a(n) for n = 1..179</a>

%F Empirical for column k:

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

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

%F k=3: [order 15]

%F k=4: a(n) = 18*a(n-2) +36*a(n-3) -45*a(n-4) -216*a(n-5) -243*a(n-6) for n>7

%F k=5: [order 84]

%F k=6: [order 36] for n>40

%F Empirical for row n:

%F n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)

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

%F n=3: [order 70]

%F n=4: [order 56]

%e Some solutions for n=4 k=4

%e ..1..2..3..4..8....1..5..6..4..8....1..5..3..4..8....1..2..3..4..8

%e ..0..7.11..9.13....0..7..2..9..3....0..7..2..9.13....0.10.11.12.13

%e ..5..6.16.17.18...11.15.16.17.18...11..6.16.17.18....5..6..7.14..9

%e .10.20.21.12.14...10.20.12.13.14...10.20.21.12.14...16.20.21.19.23

%e .15.22.23.24.19...21.22.23.24.19...15.22.23.24.19...15.22.17.24.18

%Y Column 1 is A000931(n+4).

%Y Column 2 is A000079(n-1).

%Y Row 1 is A253412(n-2).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 17 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 28 13:24 EST 2020. Contains 331321 sequences. (Running on oeis4.)