A221356 T(n,k)=Sum of neighbor maps: log base 2 of the number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 nXk array

1, 1, 2, 3, 4, 3, 4, 6, 4, 4, 4, 8, 9, 8, 5, 6, 10, 12, 12, 9, 6, 7, 12, 12, 12, 15, 12, 7, 7, 14, 18, 20, 20, 18, 12, 8, 9, 16, 21, 24, 24, 24, 21, 16, 9, 10, 18, 22, 28, 30, 30, 28, 24, 17, 10, 10, 20, 27, 32, 35, 30, 31, 32, 27, 20, 11, 12, 22, 30, 32, 39, 42, 42, 40, 32, 30, 20, 12, 13, 24

Offset

1,3

Comments

Table starts

..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16.16.18

..2..4..6..8.10.12.14.16.18.20.22.24.26.28.30.32.34

..3..4..9.12.12.18.21.22.27.30.30.36.39.40.45.48

..4..8.12.12.20.24.28.32.32.40.44.48.52.52.60

..5..9.15.20.24.30.35.39.45.50.54.60.65.69

..6.12.18.24.30.30.42.48.54.60.66.72.72

..7.12.21.28.31.42.49.54.63.70.70.84

..8.16.24.32.40.48.56.58.72.80.88

..9.17.27.32.44.54.63.71.73

.10.20.30.40.50.60.70.80

.11.20.33.44.52.66.77

.12.24.36.48.60.72

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) increment period 1: 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) = 2*a(n-1) -a(n-2) increment period 1: 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-1) +a(n-8) -a(n-9) increment period 8: 6 2 8 4 6 1 9 4

k=6: a(n) = a(n-1) +a(n-7) -a(n-8) increment period 7: 6 6 6 6 0 12 6

k=7: a(n) = 2*a(n-1) -a(n-2) increment period 1: 7

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) increment period 1: 2

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

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

n=5: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 4 6 5

n=6: a(n) = a(n-1) +a(n-7) -a(n-8) increment period 7: 6 6 6 6 0 12 6

Example

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

Crossrefs

Sequence in context: A065651 A322567 A349049 * A177329 A360379 A253852

Adjacent sequences: A221353 A221354 A221355 * A221357 A221358 A221359

Keyword

nonn,tabl

Author

R. H. Hardin Jan 12 2013

Status

approved