A269089 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

2, 4, 4, 7, 11, 7, 13, 30, 30, 13, 23, 76, 114, 76, 23, 41, 191, 428, 428, 191, 41, 72, 467, 1531, 2238, 1531, 467, 72, 126, 1127, 5387, 11314, 11314, 5387, 1127, 126, 219, 2686, 18590, 55620, 80422, 55620, 18590, 2686, 219, 379, 6339, 63347, 268289, 555789

Offset

1,1

Comments

Table starts

...2.....4......7.......13.........23..........41............72............126

...4....11.....30.......76........191.........467..........1127...........2686

...7....30....114......428.......1531........5387.........18590..........63347

..13....76....428.....2238......11314.......55620........268289........1274435

..23...191...1531....11314......80422......555789.......3761534.......25063389

..41...467...5387....55620.....555789.....5372270......50865307......473602013

..72..1127..18590...268289....3761534....50865307.....673690710.....8768989835

.126..2686..63347..1274435...25063389...473602013....8768989835...159449028034

.219..6339.213490..5982734..164926651..4353444165..112658396453..2861259712706

.379.14840.713237.27813229.1074440360.39602482120.1431998499913.50787612264272

Links

R. H. Hardin, Table of n, a(n) for n = 1..1404

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 16]

k=5: [order 26]

k=6: [order 42]

k=7: [order 68]

Example

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

Crossrefs

Column 1 is A208354(n+1).

Sequence in context: A362937 A268781 A282647 * A282862 A296578 A268750

Adjacent sequences: A269086 A269087 A269088 * A269090 A269091 A269092

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2016

Status

approved