A268995 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

2, 4, 4, 7, 13, 8, 13, 35, 41, 16, 23, 103, 174, 126, 32, 41, 278, 805, 849, 379, 64, 72, 763, 3331, 6009, 4083, 1121, 128, 126, 2037, 14080, 37987, 43512, 19416, 3272, 256, 219, 5421, 57287, 244397, 421450, 308112, 91491, 9449, 512, 379, 14264, 232449, 1506570

Offset

1,1

Comments

Table starts

....2.....4.......7........13..........23............41..............72

....4....13......35.......103.........278...........763............2037

....8....41.....174.......805........3331.........14080...........57287

...16...126.....849......6009.......37987........244397.........1506570

...32...379....4083.....43512......421450.......4097199........38241770

...64..1121...19416....308112.....4583103......66954420.......946498448

..128..3272...91491...2144780....49084071....1073436321.....22995344760

..256..9449..427863..14730784...519385102...16957258387....550731432312

..512.27049.1988142.100087792..5442503771..264744926212..13040291111728

.1024.76866.9187653.674045392.56571775611.4093941136805.305911647779632

Links

R. H. Hardin, Table of n, a(n) for n = 1..799

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)

k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7

k=5: [order 8] for n>9

k=6: [order 10] for n>12

k=7: [order 14] for n>16

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)

n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)

n=3: [order 9]

n=4: [order 16]

n=5: [order 26]

n=6: [order 42]

n=7: [order 68]

Example

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

Crossrefs

Column 1 is A000079.

Row 1 is A208354(n+1).

Sequence in context: A224409 A226870 A227751 * A205744 A237859 A240338

Adjacent sequences: A268992 A268993 A268994 * A268996 A268997 A268998

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2016

Status

approved