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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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 19 2016
STATUS
approved