A219525 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 king-move neighbors in a random 0..1 nXk array

1, 1, 1, 3, 1, 3, 4, 3, 3, 4, 4, 4, 9, 4, 4, 6, 4, 12, 12, 4, 6, 7, 6, 12, 16, 12, 6, 7, 7, 7, 18, 16, 16, 18, 7, 7, 9, 7, 21, 24, 16, 24, 21, 7, 9, 10, 9, 21, 28, 24, 24, 28, 21, 9, 10, 10, 10, 27, 28, 28, 36, 28, 28, 27, 10, 10, 12, 10, 30, 36, 28, 42, 42, 28, 36, 30, 10, 12, 13, 12, 30, 40

Offset

1,4

Comments

Table starts

..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16.16

..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16

..3..3..9.12.12.18.21.21.27.30.30.36.39.39.45

..4..4.12.16.16.24.28.28.36.40.40.48.52.52

..4..4.12.16.16.24.28.28.36.40.40.48.52

..6..6.18.24.24.36.42.42.54.60.60.72

..7..7.21.28.28.42.49.49.63.70.70

..7..7.21.28.28.42.49.49.63.70

..9..9.27.36.36.54.63.63

.10.10.30.40.40.60.70

.10.10.30.40.40.60

.12.12.36.48.48

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical: T(n,k)=3*((n-1)/3)+(n%3)^2-3*(n%3)+3+((k-1)/3)*(n*3-(((n%3)^2-(n%3))*3)/2)+((k%3)^2-3*(k%3)+2)*((n*3-(((n%3)^2-(n%3))*3)/2)/3) where '%'=modulo and '/'=integer divide truncating towards zero

Example

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

Crossrefs

Sequence in context: A081772 A204217 A296955 * A050121 A029152 A320279

Adjacent sequences: A219522 A219523 A219524 * A219526 A219527 A219528

Keyword

nonn,tabl

Author

R. H. Hardin Nov 21 2012

Status

approved