A206981 -id:A206981 - cp's OEIS frontend

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

R. H. Hardin Mar 01 2012

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

			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

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

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

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

cp's OEIS Frontend

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.

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