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A268904
T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
14
0, 3, 0, 12, 36, 0, 36, 168, 240, 0, 96, 696, 1584, 1344, 0, 240, 2664, 9720, 12960, 6912, 0, 576, 9720, 54936, 118584, 98496, 33792, 0, 1344, 34344, 299088, 1004184, 1347192, 715392, 159744, 0, 3072, 118584, 1585800, 8250912, 17194680, 14644152, 5038848
OFFSET
1,2
COMMENTS
Table starts
.0.......3........12..........36............96............240..............576
.0......36.......168.........696..........2664...........9720............34344
.0.....240......1584........9720.........54936.........299088..........1585800
.0....1344.....12960......118584.......1004184........8250912.........66210264
.0....6912.....98496.....1347192......17194680......214142760.......2611960344
.0...33792....715392....14644152.....282550680.....5344944120......99308573208
.0..159744...5038848...154472184....4513169016...129834259704....3679171151832
.0..737280..34712064..1594323000...70609114584..3091414865040..133712637011640
.0.3342336.235146240.16185567096.1087342615224.72488795124312.4788143315276472
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 8*a(n-1) -16*a(n-2)
k=3: a(n) = 12*a(n-1) -36*a(n-2)
k=4: a(n) = 18*a(n-1) -81*a(n-2) for n>3
k=5: a(n) = 30*a(n-1) -261*a(n-2) +540*a(n-3) -324*a(n-4)
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)
k=7: [order 8]
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 6*a(n-1) -9*a(n-2) for n>4
n=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>6
n=4: [order 6] for n>12
n=5: [order 14] for n>18
n=6: [order 18] for n>26
n=7: [order 54] for n>60
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..0. .0..1..2..1. .0..1..2..1. .1..0..0..0. .2..1..0..1
..0..0..0..0. .2..2..2..2. .0..1..0..0. .0..0..1..2. .2..1..2..2
..1..1..0..0. .1..0..1..0. .2..0..1..0. .1..0..0..0. .0..1..1..0
..2..1..0..0. .1..0..1..2. .1..0..0..0. .0..1..0..0. .0..0..0..0
CROSSREFS
Row 1 is A167667(n-1).
Sequence in context: A135687 A057374 A269035 * A058896 A186748 A222754
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 15 2016
STATUS
approved