A223449 - OEIS

%I #4 Mar 20 2013 07:08:09

%S 15,28,28,66,104,66,144,408,408,144,336,1616,2988,1616,336,752,6432,

%T 20640,20640,6432,752,1752,25664,149120,262368,149120,25664,1752,3936,

%U 102528,1050624,3364544,3364544,1050624,102528,3936,9168,409856,7557696

%N T(n,k)=4-level binary fanout graph coloring a rectangular array: number of nXk 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 1,3 3,5 3,6 1,4 4,7 4,8 0,2 2,9 9,11 9,12 2,10 10,13 10,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Table starts

%C ....15......28.........66...........144.............336................752

%C ....28.....104........408..........1616............6432..............25664

%C ....66.....408.......2988.........20640..........149120............1050624

%C ...144....1616......20640........262368.........3364544...........43139520

%C ...336....6432.....149120.......3364544........78731136.........1806815040

%C ...752...25664....1050624......43139520......1806815040........75601620736

%C ..1752..102528....7557696.....553773760.....42196917280......3173584196608

%C ..3936..409856...53547904....7110140800....972415126144....133184053106688

%C ..9168.1638912..384685440...91312361088..22683600827456...5592572908886016

%C .20608.6554624.2730236928.1172796624128.523428338294528.234829512186605568

%H R. H. Hardin, <a href="/A223449/b223449.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-2) -4*a(n-4)

%F k=2: a(n) = 6*a(n-1) -8*a(n-2) for n>3

%F k=3: a(n) = 70*a(n-2) -1024*a(n-4) +2832*a(n-6) -1792*a(n-8) +128*a(n-10)

%F k=4: [order 11] for n>12

%F k=5: [order 32]

%F k=6: [order 44] for n>45

%e Some solutions for n=3 k=4

%e ..2..9.12..9....2..9.11..9....7..4..1..0....0..1..3..5....9..2..0..2

%e ..9..2..9.11....9.12..9.12....4..8..4..1....1..3..6..3....2.10..2.10

%e .12..9.12..9...11..9.12..9....7..4..8..4....0..1..3..1...10..2.10.13

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013