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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 3 is A003461 for n>1.

Sequence in context: A220358 A089002 A097089 * A318075 A318343 A318024

Adjacent sequences: A317761 A317762 A317763 * A317765 A317766 A317767

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 06 2018

Status

approved