A219741 T(n,k) = Unmatched value maps: number of nXk binary arrays indicating the locations of corresponding elements not equal to any horizontal, vertical or antidiagonal neighbor in a random 0..1 nXk array.

1, 2, 2, 4, 6, 4, 7, 13, 13, 7, 12, 28, 42, 28, 12, 21, 60, 126, 126, 60, 21, 37, 129, 387, 524, 387, 129, 37, 65, 277, 1180, 2229, 2229, 1180, 277, 65, 114, 595, 3606, 9425, 13322, 9425, 3606, 595, 114, 200, 1278, 11012, 39905, 78661, 78661, 39905, 11012, 1278, 200

Offset

1,2

Comments

Table starts

...1.....2......4........7.........12...........21.............37

...2.....6.....13.......28.........60..........129............277

...4....13.....42......126........387.........1180...........3606

...7....28....126......524.......2229.........9425..........39905

..12....60....387.....2229......13322........78661.........466288

..21...129...1180.....9425......78661.......647252........5350080

..37...277...3606....39905.....466288......5350080.......61758332

..65...595..11012...168925....2760690.....44159095......711479843

.114..1278..33636...715072...16350693....364647622.....8201909757

.200..2745.102733..3027049...96830726...3010723330....94531063074

.351..5896.313781.12813931..573456240..24858935864..1089590912023

.616.12664.958384.54243509.3396136349.205253857220.12558669019786

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Zeilberger's Maple code (see links in A228285) would presumably give recurrences for the columns of this array. - N. J. A. Sloane, Aug 22 2013

Example

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

Crossrefs

Column 1 is A005251(n+2).

Column 2 is A002478(n+1).

Column 3 is A105262(n+1) for n>1.

Main diagonal is A066864.

See A226444 for an array with very similar entries. - N. J. A. Sloane, Aug 22 2013

Sequence in context: A350229 A085730 A232065 * A210603 A252820 A218765

Adjacent sequences: A219738 A219739 A219740 * A219742 A219743 A219744

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2012

Status

approved