A206063 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two clockwise edge increases

256, 2184, 2184, 19832, 21140, 19832, 170688, 167960, 167960, 170688, 1499080, 1390488, 1278672, 1390488, 1499080, 13136860, 11638960, 11155584, 11155584, 11638960, 13136860, 114770680, 96831504, 101369476, 111242648, 101369476

Offset

1,1

Comments

Table starts

........256.......2184.......19832........170688........1499080

.......2184......21140......167960.......1390488.......11638960

......19832.....167960.....1278672......11155584......101369476

.....170688....1390488....11155584.....111242648.....1198231144

....1499080...11638960...101369476....1198231144....18209383140

...13136860...96831504...910785080...12877680064...265284773176

..114770680..805817696..8150091296..144759802024..4049733446192

.1005245456.6714115792.73102971728.1569116858248.62573461436920

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) +34*a(n-2) +145*a(n-3) -18*a(n-4) -2*a(n-5) +11*a(n-6) +6*a(n-7) +2*a(n-8) +4*a(n-9) for n>10

k=2: a(n) = 3*a(n-1) +20*a(n-2) +189*a(n-3) +102*a(n-4) +187*a(n-5) -612*a(n-6) -110*a(n-7) +186*a(n-8) +82*a(n-9) +43*a(n-10) -5*a(n-11) -16*a(n-12) for n>17

k=3: a(n) = a(n-2) +695*a(n-3) +2*a(n-4) +1693*a(n-5) -1278*a(n-7) +682*a(n-9) +286*a(n-11) +32*a(n-13) for n>20

k=4: a(n) = 1307*a(n-3) +24*a(n-4) +677*a(n-5) +44*a(n-6) +256*a(n-7) for n>16

k=5: a(n) = 3457*a(n-3) +526*a(n-5) for n>14

k=6: a(n) = 9491*a(n-3) +213*a(n-5) for n>15

k=7: a(n) = 26761*a(n-3) +573*a(n-5) for n>16

Example

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

Crossrefs

Sequence in context: A237076 A237069 A346961 * A206056 A207799 A207792

Adjacent sequences: A206060 A206061 A206062 * A206064 A206065 A206066

Keyword

nonn,tabl

Author

R. H. Hardin Feb 03 2012

Status

approved