A269075 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

2, 4, 4, 7, 11, 8, 13, 27, 32, 16, 23, 76, 123, 89, 32, 41, 185, 521, 537, 244, 64, 72, 489, 1887, 3288, 2343, 659, 128, 126, 1204, 7477, 17713, 20400, 10167, 1760, 256, 219, 3059, 27042, 102545, 165607, 123976, 43959, 4657, 512, 379, 7539, 102070, 542112

Offset

1,1

Comments

Table starts

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

....4....11......27........76.........185..........489...........1204

....8....32.....123.......521........1887.........7477..........27042

...16....89.....537......3288.......17713.......102545.........542112

...32...244....2343.....20400......165607......1383105.......10778640

...64...659...10167....123976.....1529241.....18220241......210476400

..128..1760...43959....742688....14011359....236272677.....4064720816

..256..4657..189465...4397376...127528641...3024972401....77785162880

..512.12228..814359..25791040..1154377943..38333973609..1477636398784

.1024.31899.3491691.150081504.10400164377.481701017577.27897108860960

Links

R. H. Hardin, Table of n, a(n) for n = 1..721

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)

k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7

k=5: [order 12]

k=6: [order 14]

k=7: [order 24] for n>25

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) -6*a(n-3) -9*a(n-4)

n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)

n=4: [order 8]

n=5: [order 14]

Example

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

Crossrefs

Column 1 is A000079.

Column 2 is A268744.

Row 1 is A208354(n+1).

Sequence in context: A295275 A295253 A295652 * A283543 A297682 A297607

Adjacent sequences: A269072 A269073 A269074 * A269076 A269077 A269078

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2016

Status

approved