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A269201
T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.
13
4, 16, 16, 60, 180, 64, 216, 1284, 1740, 256, 756, 9612, 25572, 15540, 1024, 2592, 68052, 400428, 471492, 132300, 4096, 8748, 472044, 5877228, 15289548, 8314020, 1090740, 16384, 29160, 3212820, 84310620, 463790340, 555862380, 142233732
OFFSET
1,1
COMMENTS
Table starts
.......4.........16.............60...............216..................756
......16........180...........1284..............9612................68052
......64.......1740..........25572............400428..............5877228
.....256......15540.........471492..........15289548............463790340
....1024.....132300........8314020.........555862380..........34838403756
....4096....1090740......142233732.......19558138380........2532677348772
...16384....8787660.....2380537188......672230393004......179867149105740
...65536...69580980....39186271044....22702294138188....12551707872624132
..262144..543538380...636703584804...756261535626732...864008559706781292
.1048576.4200069300.10237337586180.24917784636315276.58827234014669683044
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1)
k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5
k=4: [order 6] for n>7
k=5: [order 20] for n>21
k=6: [order 42] for n>43
Empirical for row n:
n=1: a(n) = 6*a(n-1) -9*a(n-2)
n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)
n=3: [order 8]
n=4: [order 20]
n=5: [order 52] for n>53
EXAMPLE
Some solutions for n=3 k=4
..2..2..0..0. .2..2..1..1. .2..0..0..1. .0..0..2..2. .2..2..2..2
..1..0..0..2. .2..0..0..0. .0..2..0..2. .2..2..2..2. .0..0..0..1
..2..0..2..0. .1..0..0..0. .1..0..2..0. .1..0..0..2. .1..1..1..1
CROSSREFS
Column 1 is A000302.
Column 2 is A269103.
Row 1 is A120926(n+1).
Sequence in context: A269194 A269143 A269109 * A269289 A267933 A206974
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 20 2016
STATUS
approved