A208780 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 1 vertically

2, 4, 4, 6, 16, 6, 10, 36, 36, 10, 16, 100, 36, 100, 16, 26, 256, 60, 60, 256, 26, 42, 676, 96, 100, 96, 676, 42, 68, 1764, 156, 160, 160, 156, 1764, 68, 110, 4624, 252, 260, 256, 260, 252, 4624, 110, 178, 12100, 408, 420, 416, 416, 420, 408, 12100, 178, 288, 31684, 660

Offset

1,1

Comments

Table starts

..2....4...6..10...16...26...42...68...110...178...288....466....754....1220

..4...16..36.100..256..676.1764.4624.12100.31684.82944.217156.568516.1488400

..6...36..36..60...96..156..252..408...660..1068..1728...2796...4524....7320

.10..100..60.100..160..260..420..680..1100..1780..2880...4660...7540...12200

.16..256..96.160..256..416..672.1088..1760..2848..4608...7456..12064...19520

.26..676.156.260..416..676.1092.1768..2860..4628..7488..12116..19604...31720

.42.1764.252.420..672.1092.1764.2856..4620..7476.12096..19572..31668...51240

.68.4624.408.680.1088.1768.2856.4624..7480.12104.19584..31688..51272...82960

Links

R. H. Hardin, Table of n, a(n) for n = 1..10018

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

k=3: a(n) = a(n-1) +a(n-2) for n>4

k=4: a(n) = a(n-1) +a(n-2) for n>4

k=5: a(n) = a(n-1) +a(n-2) for n>4

k=6: a(n) = a(n-1) +a(n-2) for n>4

k=7: a(n) = a(n-1) +a(n-2) for n>4

Example

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

Crossrefs

Column 1 is A006355(n+2)

Column 2 is A206981

Diagonal is A206981 and column 2 for n>1

Column 3 is A022346(n+1) for n>2

Column 4 is A022354(n+1) for n>2

Column 5 is A022366(n+1) for n>2

Sequence in context: A208369 A207717 A208078 * A206987 A207845 A207808

Adjacent sequences: A208777 A208778 A208779 * A208781 A208782 A208783

Keyword

nonn,tabl

Author

R. H. Hardin Mar 01 2012

Status

approved