

A206215


T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..2 introduced in row major order


9



14, 45, 45, 162, 130, 162, 594, 336, 336, 594, 2268, 992, 760, 992, 2268, 8802, 2996, 2224, 2224, 2996, 8802, 34236, 9072, 5632, 8136, 5632, 9072, 34236, 133974, 27656, 14416, 21984, 21984, 14416, 27656, 133974, 525636, 84152, 40032, 74080, 86152
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OFFSET

1,1


COMMENTS

Table starts
.....14....45....162....594....2268.....8802.....34236.....133974......525636
.....45...130....336....992....2996.....9072.....27656......84152......256416
....162...336....760...2224....5632....14416.....40032.....101376......259488
....594...992...2224...8136...21984....74080....274320.....747456.....2518720
...2268..2996...5632..21984...86152...359424...1435584....5673232....23721984
...8802..9072..14416..74080..359424..1764000...9438912...46540800...228988224
..34236.27656..40032.274320.1435584..9438912..68074272..366583680..2427719040
.133974.84152.101376.747456.5673232.46540800.366583680.2870491680.23806365696


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..840


FORMULA

Empirical for column k:
k=1: a(n) = 4*a(n1) a(n2) +12*a(n3) 36*a(n4) for n>5
k=2: a(n) = a(n1) +6*a(n2) +4*a(n3) 10*a(n4) for n>6
k=3: a(n) = 18*a(n3) for n>6
k=4: a(n) = 34*a(n3) for n>7
k=5: a(n) = 66*a(n3) for n>8
k=6: a(n) = 130*a(n3) for n>9
k=7: a(n) = 258*a(n3) for n>10
apparently a(n) = (2^(k+1) +2)*a(n3) for k>2 and n>k+3


EXAMPLE

Some solutions for n=4 k=3
..0..1..0..2....0..0..1..2....0..0..1..2....0..0..1..0....0..0..1..1
..1..0..0..2....2..0..0..1....0..1..2..2....0..1..0..0....2..2..0..1
..0..0..1..0....0..2..0..0....1..2..2..0....1..0..0..2....0..2..2..0
..0..2..0..0....0..0..1..0....2..2..0..1....0..0..1..0....1..0..2..2
..2..0..0..1....1..0..0..1....2..0..1..1....0..1..0..0....1..1..0..0


CROSSREFS

Sequence in context: A215199 A216258 A064348 * A328243 A123295 A092350
Adjacent sequences: A206212 A206213 A206214 * A206216 A206217 A206218


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin Feb 04 2012


STATUS

approved



