A268904 - OEIS

%I #4 Feb 15 2016 14:58:49

%S 0,3,0,12,36,0,36,168,240,0,96,696,1584,1344,0,240,2664,9720,12960,

%T 6912,0,576,9720,54936,118584,98496,33792,0,1344,34344,299088,1004184,

%U 1347192,715392,159744,0,3072,118584,1585800,8250912,17194680,14644152,5038848

%N T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

%C Table starts

%C .0.......3........12..........36............96............240..............576

%C .0......36.......168.........696..........2664...........9720............34344

%C .0.....240......1584........9720.........54936.........299088..........1585800

%C .0....1344.....12960......118584.......1004184........8250912.........66210264

%C .0....6912.....98496.....1347192......17194680......214142760.......2611960344

%C .0...33792....715392....14644152.....282550680.....5344944120......99308573208

%C .0..159744...5038848...154472184....4513169016...129834259704....3679171151832

%C .0..737280..34712064..1594323000...70609114584..3091414865040..133712637011640

%C .0.3342336.235146240.16185567096.1087342615224.72488795124312.4788143315276472

%H R. H. Hardin, <a href="/A268904/b268904.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

%F k=2: a(n) = 8*a(n-1) -16*a(n-2)

%F k=3: a(n) = 12*a(n-1) -36*a(n-2)

%F k=4: a(n) = 18*a(n-1) -81*a(n-2) for n>3

%F k=5: a(n) = 30*a(n-1) -261*a(n-2) +540*a(n-3) -324*a(n-4)

%F k=6: a(n) = 50*a(n-1) -805*a(n-2) +4662*a(n-3) -12150*a(n-4) +14580*a(n-5) -6561*a(n-6)

%F k=7: [order 8]

%F Empirical for row n:

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

%F n=2: a(n) = 6*a(n-1) -9*a(n-2) for n>4

%F n=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>6

%F n=4: [order 6] for n>12

%F n=5: [order 14] for n>18

%F n=6: [order 18] for n>26

%F n=7: [order 54] for n>60

%e Some solutions for n=4 k=4

%e ..1..0..0..0. .0..1..2..1. .0..1..2..1. .1..0..0..0. .2..1..0..1

%e ..0..0..0..0. .2..2..2..2. .0..1..0..0. .0..0..1..2. .2..1..2..2

%e ..1..1..0..0. .1..0..1..0. .2..0..1..0. .1..0..0..0. .0..1..1..0

%e ..2..1..0..0. .1..0..1..2. .1..0..0..0. .0..1..0..0. .0..0..0..0

%Y Row 1 is A167667(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 15 2016