A270150 - OEIS

%I #4 Mar 12 2016 08:46:36

%S 0,8,8,112,1440,112,1176,85056,85056,1176,10976,4126368,24250368,

%T 4126368,10976,96040,182257536,5750902944,5750902944,182257536,96040,

%U 806736,7623445344,1246566350496,6697695002208,1246566350496,7623445344,806736

%N T(n,k)=Number of nXk 0..7 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling seven exactly once.

%C Table starts

%C .....0..........8.............112................1176....................10976

%C .....8.......1440...........85056.............4126368................182257536

%C ...112......85056........24250368..........5750902944............1246566350496

%C ..1176....4126368......5750902944.......6697695002208.........7142783643783792

%C .10976..182257536...1246566350496....7142783643783792.....37516051668350707200

%C .96040.7623445344.256330155581328.7232246139319438944.187171034679828236009184

%H R. H. Hardin, <a href="/A270150/b270150.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 14*a(n-1) -49*a(n-2)

%F k=2: a(n) = 66*a(n-1) -1021*a(n-2) -2244*a(n-3) -1156*a(n-4) for n>5

%F k=3: [order 10] for n>11

%F k=4: [order 30] for n>31

%e Some solutions for n=2 k=4

%e ..0..4..7..5. .0..2..6..2. .0..3..1..1. .0..0..4..7. .0..2..7..6

%e ..0..4..2..1. .0..5..0..6. .0..6..5..1. .0..0..4..0. .4..2..4..0

%Y Column 1 is A270111.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 12 2016