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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 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A214613 A325933

Adjacent sequences:  A221105 A221106 A221107 * A221109 A221110 A221111

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 02 2013

STATUS

approved

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Last modified September 18 09:56 EDT 2019. Contains 327169 sequences. (Running on oeis4.)