A221028 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, vertical and antidiagonal neighbors in a random 0..1 n X k array.

1, 1, 1, 3, 3, 3, 4, 6, 6, 4, 4, 6, 7, 6, 4, 6, 10, 11, 11, 10, 6, 7, 11, 14, 16, 14, 11, 7, 7, 13, 17, 20, 20, 17, 13, 7, 9, 16, 19, 21, 24, 21, 19, 16, 9, 10, 16, 24, 27, 30, 30, 27, 24, 16, 10, 10, 20, 27, 31, 35, 33, 35, 31, 27, 20, 10, 12, 21, 30, 33, 40, 42, 42, 40, 33, 30, 21, 12, 13

Offset

1,4

Comments

Table starts

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

..1..3..6..6.10.11.13.16.16.20.21.23.26.26.30.31.33

..3..6..7.11.14.17.19.24.27.30.30.36.39.42.43.47

..4..6.11.16.20.21.27.31.33.40.44.47.50.56.60

..4.10.14.20.24.30.35.40.42.48.55.59.62.69

..6.11.17.21.30.33.42.46.54.60.66.71.75

..7.13.19.27.35.42.45.53.62.69.72.83

..7.16.24.31.40.46.53.63.69.79.87

..9.16.27.33.42.54.62.69.81

.10.20.30.40.48.60.69.79

.10.21.30.44.55.66.72

.12.23.36.47.59.71

Links

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

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-5) -a(n-6) increment period 5: 2 3 0 4 1

k=3: a(n) = a(n-1) +a(n-12) -a(n-13) increment period 12: 3 1 4 3 3 2 5 3 3 0 6 3

k=4: a(n) = a(n-1) +a(n-17) -a(n-18) increment period 17: 2 5 5 4 1 6 4 2 7 4 3 3 6 4 0 8 4

k=5: a(n) = a(n-1) +a(n-30) -a(n-31) increment period 30: 6 4 6 4 6 5 5 2 6 7 4 3 7 3 7 6 3 4 8 5 5 4 6 4 6 4 6 0 10 4

Example

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

Crossrefs

Column 1 is A117571.

Sequence in context: A022877 A361247 A151554 * A334940 A011978 A167025

Adjacent sequences: A221025 A221026 A221027 * A221029 A221030 A221031

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2012

Status

approved