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

Author

R. H. Hardin, Feb 19 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A208354(n+1).

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]