A206118 T(n,k) = number of (n+1) X (k+1) 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two counterclockwise and two clockwise edge increases.

256, 1140, 1140, 6028, 5228, 6028, 31756, 22624, 22624, 31756, 171564, 111552, 88596, 111552, 171564, 973388, 588840, 520800, 520800, 588840, 973388, 5538732, 3048096, 2408480, 5048352, 2408480, 3048096, 5538732, 31668844, 16072760

Offset

1,1

Comments

Table starts

......256.....1140......6028......31756.......171564........973388

.....1140.....5228.....22624.....111552.......588840.......3048096

.....6028....22624.....88596.....520800......2408480......10792800

....31756...111552....520800....5048352.....21702240.....157206240

...171564...588840...2408480...21702240....190349280....1990281312

...973388..3048096..10792800..157206240...1990281312...24408220320

..5538732.16072760..59892000.1542266208..18371031840..373319837280

.31668844.84203240.276975200.6705992160.163028308320.4839970998240

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for row k:

k=1: a(n) = 5*a(n-1) + 5*a(n-2) + 29*a(n-3) - 142*a(n-4) - 248*a(n-5) + 88*a(n-6) + 144*a(n-7).

k=2: a(n) = 2*a(n-1) + 19*a(n-2) + 6*a(n-3) - 90*a(n-4) + 19*a(n-5) + 45*a(n-6) for n>8.

k=3: a(n) = 115*a(n-3) for n>6.

k=4: a(n) = 309*a(n-3) for n>7.

k=5: a(n) = 859*a(n-3) for n>8.

k=6: a(n) = 2445*a(n-3) for n>9.

k=7: a(n) = 7075*a(n-3) for n>10.

k=8: a(n) = 20709*a(n-3) for n>11.

k=9: a(n) = 61099*a(n-3) for n>12.

k=10: a(n) = 181245*a(n-3) for n>13.

Apparently, a(n) = A183624(k)*a(n-3) for k>2 and n>k+3

Example

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

Crossrefs

Sequence in context: A237688 A237299 A237293 * A206111 A237211 A237204

Adjacent sequences: A206115 A206116 A206117 * A206119 A206120 A206121

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 03 2012

Status

approved