A022346 -id:A022346 - cp's OEIS frontend

A208085 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

8, 20, 12, 56, 20, 24, 164, 32, 56, 36, 488, 52, 134, 60, 72, 1460, 84, 344, 96, 168, 108, 4376, 136, 888, 156, 402, 180, 216, 13124, 220, 2318, 252, 1032, 288, 504, 324, 39368, 356, 6056, 408, 2664, 468, 1206, 540, 648, 118100, 576, 15848, 660, 6954, 756, 3096

Offset: 1

R. H. Hardin Feb 23 2012

Table starts
...8..20...56..164..488..1460..4376..13124..39368.118100..354296.1062884
..12..20...32...52...84...136...220....356....576....932....1508....2440
..24..56..134..344..888..2318..6056..15848..41478.108584..284264..744206
..36..60...96..156..252...408...660...1068...1728...2796....4524....7320
..72.168..402.1032.2664..6954.18168..47544.124434.325752..852792.2232618
.108.180..288..468..756..1224..1980...3204...5184...8388...13572...21960
.216.504.1206.3096.7992.20862.54504.142632.373302.977256.2558376.6697854
.324.540..864.1404.2268..3672..5940...9612..15552..25164...40716...65880

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

R. H. Hardin, Table of n, a(n) for n = 1..5596

Column 1 is A153339(n+2).
Row 1 is A115099.
Row 2 is A022087(n+3).
Row 4 is A022346(n+3).

Empirical for column k:
k=1: a(n) = 3*a(n-2)
k=2..7: a(n) = 3*a(n-2) for n>3
Empirical for row n:
n=1: a(k)=4*a(k-1)-3*a(k-2)
n=2,4,6: a(k)=a(k-1)+a(k-2)
n=3,5,7: a(k)=3*a(k-1)-3*a(k-3)+a(k-4)

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.

Original entry on oeis.org

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

A208085 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula