A220196 T(n,k) = Sum of neighbor maps: log base 2 of the number of n X k binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal and vertical neighbors in a random 0..1 n X k array.

1, 1, 1, 3, 4, 3, 4, 4, 4, 4, 4, 8, 9, 8, 4, 6, 9, 12, 12, 9, 6, 7, 12, 12, 12, 12, 12, 7, 7, 12, 18, 20, 20, 18, 12, 7, 9, 16, 21, 24, 23, 24, 21, 16, 9, 10, 17, 22, 28, 30, 30, 28, 22, 17, 10, 10, 20, 27, 32, 31, 36, 31, 32, 27, 20, 10, 12, 20, 30, 32, 39, 42, 42, 39, 32, 30, 20, 12, 13, 24

Offset

1,4

Comments

Table starts

..1..1..3..4..4..6..7..7..9..10.10..12.13.13.15.16.16.18.19.19

..1..4..4..8..9.12.12.16.17..20.20..24.25.28.28.32.33.36.36

..3..4..9.12.12.18.21.22.27..30.30..36.39.40.45.48.48.54

..4..8.12.12.20.24.28.32.32..40.44..48.52.52.60.64.68

..4..9.12.20.23.30.31.39.44..50.51..60.64.69.71.80

..6.12.18.24.30.36.42.42.54..60.66..72.78.84.90

..7.12.21.28.31.42.49.54.63..70.70..84.91.96

..7.16.22.32.39.42.54.64.71..80.86..96.97

..9.17.27.32.44.54.63.71.73..90.98.108

.10.20.30.40.50.60.70.80.90.100

.10.20.30.44.51.66.70.86.98

.12.24.36.48.60.72.84.96

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 0 2 1

k=2: a(n) = a(n-1) +a(n-4) -a(n-5) increment period 4: 3 0 4 1

k=3: a(n) = a(n-1) +a(n-6) -a(n-7) increment period 6: 1 5 3 0 6 3

k=4: a(n) = a(n-1) +a(n-5) -a(n-6) increment period 5: 4 4 0 8 4

k=5: a(n) = a(n-3) +a(n-8) -a(n-11) increment period 24: 5 3 8 3 7 1 8 5 6 1 9 4 5 2 9 3 7 2 7 5 6 0 10 4

k=6: a(n) = a(n-1) +a(n-9) -a(n-10) increment period 9: 6 6 6 6 6 6 0 12 6

k=7: a(n) = a(n-1) +a(n-12) -a(n-13) increment period 12: 5 9 7 3 11 7 5 9 7 0 14 7

Example

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

Crossrefs

Column 1 is A117571.

Sequence in context: A052384 A276867 A100867 * A128200 A258168 A061988

Adjacent sequences: A220193 A220194 A220195 * A220197 A220198 A220199

Keyword

nonn,tabl

Author

R. H. Hardin Dec 07 2012

Status

approved