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

Author

R. H. Hardin, Feb 17 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079.

Row 1 is A208354(n+1).

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]