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A269035
T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
13
0, 3, 0, 12, 24, 0, 36, 48, 120, 0, 96, 216, 348, 504, 0, 240, 672, 2166, 2136, 1944, 0, 576, 2208, 9528, 18384, 12228, 7128, 0, 1344, 6912, 44760, 115656, 146064, 67104, 25272, 0, 3072, 21408, 198816, 785124, 1326576, 1114848, 357756, 87480, 0, 6912, 65280
OFFSET
1,2
COMMENTS
Table starts
.0......3.......12.........36...........96............240.............576
.0.....24.......48........216..........672...........2208............6912
.0....120......348.......2166.........9528..........44760..........198816
.0....504.....2136......18384.......115656.........785124.........4998648
.0...1944....12228.....146064......1326576.......13031664.......119790816
.0...7128....67104....1114848.....14710368......208867428......2783857776
.0..25272...357756....8277072....159397596.....3266423688.....63310818360
.0..87480..1867560...60218112...1698064656....50155587360...1416701634552
.0.297432..9593844..431354928..17853542544...759280601376..31304407671636
.0.997272.48665904.3052215072.185754411168.11364951702132.684763778434512
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
k=5: [order 12] for n>13
k=6: [order 18] for n>19
k=7: [order 38] for n>39
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
n=4: [order 12] for n>14
n=5: [order 20] for n>22
n=6: [order 46] for n>48
n=7: [order 92] for n>94
EXAMPLE
Some solutions for n=4 k=4
..2..1..0..0. .0..0..1..0. .0..1..0..1. .2..0..0..1. .2..2..2..1
..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..1. .1..2..2..2
..2..1..0..1. .0..1..0..0. .2..1..0..1. .2..1..0..1. .2..2..2..2
..0..0..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .1..1..2..2
CROSSREFS
Column 2 is A268633.
Row 1 is A167667(n-1).
Sequence in context: A269880 A135687 A057374 * A268904 A058896 A186748
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 18 2016
STATUS
approved