A221108 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 and antidiagonal neighbors in a random 0..1 nXk array

1, 1, 2, 3, 4, 3, 4, 4, 6, 4, 4, 8, 7, 7, 5, 6, 10, 11, 10, 10, 6, 7, 12, 14, 14, 13, 12, 7, 7, 12, 17, 18, 19, 16, 13, 8, 9, 16, 19, 23, 24, 24, 19, 16, 9, 10, 18, 24, 28, 28, 30, 28, 22, 18, 10, 10, 20, 27, 32, 32, 34, 35, 31, 25, 19, 11, 12, 20, 30, 32, 40, 40, 42, 40, 34, 28, 22, 12, 13

Offset

1,3

Comments

Table starts

..1..1..3..4..4..6..7..7...9..10..10..12.13.13..15.16.16.18.19.19.21

..2..4..4..8.10.12.12.16..18..20..20..24.26.28..28.32.34.36.36.40

..3..6..7.11.14.17.19.24..27..30..30..36.39.42..43.47.50.53.55

..4..7.10.14.18.23.28.32..32..40..44..47.50.54..58.63.68.72

..5.10.13.19.24.28.32.40..45..50..53..60.65.70..72.78.84

..6.12.16.24.30.34.40.48..52..58..66..72.76.84..90.96

..7.13.19.28.35.42.47.56..61..68..76..82.89.98.103

..8.16.22.31.40.48.54.62..72..80..88..96.98

..9.18.25.34.44.54.61.70..77..88..97.108

.10.19.28.39.48.58.68.80..90.100.108

.11.22.31.44.54.66.75.87..97.108

.12.24.34.48.60.71.82.96.106

Links

R. H. Hardin, Table of n, a(n) for n = 1..217

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

k=3: a(n) = 2*a(n-1) -a(n-2) for n>3 increment period of length 1: 3

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

k=5: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) +2*a(n-5) -a(n-6) for n>7 increment period of length 6: 4 4 6 6 5 5

k=6: a(n) = a(n-1) +a(n-9) -a(n-10) for n>11 increment period of length 9: 5 6 5 6 8 6 6 4 8

k=7: a(n) = 2*a(n-1) -a(n-2) for n>7 increment period of length 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) = a(n-1) +a(n-4) -a(n-5) increment period 4: 2 0 4 2

n=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

n=4: a(n) = a(n-1) +a(n-10) -a(n-11) increment period 10: 3 3 4 4 5 5 4 0 8 4

n=5: a(n) = a(n-1) +a(n-24) -a(n-25) increment period 24: 5 3 6 5 4 4 8 5 5 3 7 5 5 2 6 6 5 4 7 5 5 0 10 5

n=6: a(n) = 2*a(n-1) -a(n-2) -a(n-3) +2*a(n-4) -a(n-5) -a(n-6) +2*a(n-7) -a(n-8) -a(n-9) +2*a(n-10) -a(n-11) -a(n-12) +2*a(n-13) -a(n-14) -a(n-15) +2*a(n-16) -a(n-17) increment period 18: 6 4 8 6 4 6 8 4 6 8 6 4 8 6 6 0 12 6

Example

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

Crossrefs

Sequence in context: A030583 A030563 A081399 * A205554 A336750 A336755

Adjacent sequences: A221105 A221106 A221107 * A221109 A221110 A221111

Keyword

nonn,tabl

Author

R. H. Hardin Jan 02 2013

Status

approved