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A206238 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order 9
15, 60, 60, 310, 256, 310, 1640, 1136, 1136, 1640, 8910, 5728, 4456, 5728, 8910, 51066, 31652, 27168, 27168, 31652, 51066, 294546, 170728, 133392, 283728, 133392, 170728, 294546, 1710184, 943584, 607008, 1236432, 1236432, 607008, 943584, 1710184 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

......15......60......310......1640........8910........51066........294546

......60.....256.....1136......5728.......31652.......170728........943584

.....310....1136.....4456.....27168......133392.......607008.......3503136

....1640....5728....27168....283728.....1236432......9042600......95322432

....8910...31652...133392...1236432....10915392....118573968....1122086640

...51066..170728...607008...9042600...118573968...1448239080...22535636736

..294546..943584..3503136..95322432..1122086640..22535636736..649065145152

.1710184.5175034.17206032.419146392.10022726928.303011941944.8026428934128

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..544

FORMULA

Empirical for column k:

k=1: a(n) = 8*a(n-1) -11*a(n-2) +36*a(n-3) -303*a(n-4) +232*a(n-5) +147*a(n-6) +756*a(n-7) for n>8

k=2: a(n) = 3*a(n-1) +20*a(n-2) -14*a(n-3) -133*a(n-4) +95*a(n-5) +123*a(n-6) +9*a(n-7) -102*a(n-8) for n>10

k=3: a(n) = a(n-1) +129*a(n-3) -129*a(n-4) for n>7

k=4: a(n) = a(n-1) +339*a(n-3) -339*a(n-4) for n>8

k=5: a(n) = a(n-1) +921*a(n-3) -921*a(n-4) for n>9

k=6: a(n) = a(n-1) +2571*a(n-3) -2571*a(n-4) for n>10

k=7: a(n) = a(n-1) +7329*a(n-3) -7329*a(n-4) for n>11

k=8: a(n) = a(n-1) +21219*a(n-3) -21219*a(n-4) for n>12

k=9: a(n) = a(n-1) +62121*a(n-3) -62121*a(n-4) for n>13

k=10: a(n) = a(n-1) +183291*a(n-3) -183291*a(n-4) for n>14

k=11: a(n) = a(n-1) +543729*a(n-3) -543729*a(n-4) for n>15

apparently a(n) = a(n-1) +3*A085279(k+1)*a(n-3) -3*A085279(k+1)*a(n-4) for k>2 and n>k+4

EXAMPLE

Some solutions for n=4 k=3

..0..0..1..0....0..0..1..1....0..0..1..1....0..1..2..0....0..0..1..1

..0..1..0..0....0..2..3..3....2..2..3..1....3..2..2..0....2..2..0..1

..2..0..0..1....2..3..3..2....1..2..2..3....2..2..1..2....3..2..2..3

..0..0..2..3....3..3..0..3....0..1..2..2....2..1..2..2....2..1..2..2

..0..1..3..3....0..0..3..3....0..0..3..2....3..2..2..3....2..2..0..2

CROSSREFS

Sequence in context: A261798 A022287 A223344 * A064761 A005945 A223337

Adjacent sequences:  A206235 A206236 A206237 * A206239 A206240 A206241

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Feb 05 2012

STATUS

approved

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Last modified May 23 18:42 EDT 2017. Contains 286926 sequences.