A317764 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 16, 20, 16, 32, 42, 28, 28, 42, 32, 64, 89, 52, 43, 52, 89, 64, 128, 190, 100, 72, 72, 100, 190, 128, 256, 407, 196, 127, 109, 127, 196, 407, 256, 512, 873, 388, 232, 177, 177, 232, 388, 873, 512, 1024, 1874, 772, 432, 302, 266, 302

Offset: 1

Author

R. H. Hardin, Aug 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1...2...4...8..16...32...64..128..256..512.1024..2048..4096..8192.16384

...2...6..10..20..42...89..190..407..873.1874.4024..8642.18561.39866.85627

...4..10..16..28..52..100..196..388..772.1540.3076..6148.12292.24580.49156

...8..20..28..43..72..127..232..432..813.1539.2922..5557.10577.20141.38362

..16..42..52..72.109..177..302..532..955.1733.3164..5796.10637.19541.35918

..32..89.100.127.177..266..425..709.1217.2126.3753..6666.11882.21223.37952

..64.190.196.232.302..425..639.1012.1663.2801.4792..8278.14385.25088.43852

.128.407.388.432.532..709.1012.1529.2413.3927.6524.10984.18651.31842.54552

.256.873.772.813.955.1217.1663.2413.3674.5798.9381.15434.25672.43007.72386

Examples

			Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..1..1..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..1. .1..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0
..0..0..0..0. .1..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1300

Crossrefs

Column 1 is A000079(n-1).

Column 3 is A003461 for n>1.

Formula

Empirical for column k:

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

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

k=3: a(n) = 3*a(n-1) -2*a(n-2) for n>3

k=4: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) +a(n-5) for n>6

k=5: a(n) = 2*a(n-1) -a(n-4) for n>6

k=6: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) +a(n-7) for n>10

k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-4) +a(n-5) -a(n-6) +a(n-7) for n>11