A237234 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

81, 268, 268, 928, 984, 928, 2784, 3284, 3284, 2784, 9628, 10888, 12014, 10888, 9628, 28912, 36180, 29456, 29456, 36180, 28912, 100008, 120540, 97862, 83436, 97862, 120540, 100008, 300256, 401520, 269844, 233536, 233536, 269844, 401520, 300256

Offset

1,1

Comments

Table starts

......81......268......928.....2784.....9628.....28912....100008.....300256

.....268......984.....3284....10888....36180....120540....401520....1336540

.....928.....3284....12014....29456....97862....269844....926086....2450048

....2784....10888....29456....83436...233536....671080...1919288....5542856

....9628....36180....97862...233536...721854...1737372...5299502...12992080

...28912...120540...269844...671080..1737372...5016852..13078228...34663620

..100008...401520...926086..1919288..5299502..13078228..42143930...92484308

..300256..1336540..2450048..5542856.12992080..34663620..92484308..257895268

.1038560..4448892..8256930.15833748.40059070..93075252.270710424..650555580

.3118208.14811704.22301740.45309424.97555340.252437984.638608676.1691829676

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-2) +24*a(n-4) +8*a(n-6) for n>7

k=2: a(n) = a(n-1) +4*a(n-2) +5*a(n-3) +21*a(n-4) +12*a(n-5) +4*a(n-6) for n>8

k=3: a(n) = 5*a(n-2) +42*a(n-4) -21*a(n-6) -207*a(n-8) for n>13

k=4: [order 13] for n>16

k=5: [order 26] for n>29

k=6: [order 34] for n>40

k=7: [order 56] for n>63

Example

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

Crossrefs

Sequence in context: A237630 A236746 A236739 * A237227 A206094 A202333

Adjacent sequences: A237231 A237232 A237233 * A237235 A237236 A237237

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2014

Status

approved