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T(n,k) = Number of n X k binary arrays with each 1 adjacent to exactly two 0's.
7

%I #9 May 19 2020 15:12:32

%S 1,1,1,2,7,2,3,10,10,3,5,23,26,23,5,8,49,66,66,49,8,13,98,194,247,194,

%T 98,13,21,209,534,899,899,534,209,21,34,431,1468,3254,4643,3254,1468,

%U 431,34,55,898,4102,11883,21708,21708,11883,4102,898,55,89,1871,11402,43207

%N T(n,k) = Number of n X k binary arrays with each 1 adjacent to exactly two 0's.

%C Table starts

%C ..1....1.....2......3........5.........8.........13..........21...........34

%C ..1....7....10.....23.......49........98........209.........431..........898

%C ..2...10....26.....66......194.......534.......1468........4102........11402

%C ..3...23....66....247......899......3254......11883.......43207.......157266

%C ..5...49...194....899.....4643.....21708.....104651......506385......2433550

%C ..8...98...534...3254....21708....135578.....863096.....5518572.....35095832

%C .13..209..1468..11883...104651....863096....7279940....61405393....515820700

%C .21..431..4102..43207...506385...5518572...61405393...684911503...7604015546

%C .34..898.11402.157266..2433550..35095832..515820700..7604015546.111613234643

%C .55.1871.31644.572571.11727959.223543018.4341917265.84593723891

%H R. H. Hardin, <a href="/A183335/b183335.txt">Table of n, a(n) for n = 1..337</a>

%e Some solutions for 7 X 6

%e ..0..1..0..0..0..0....0..0..0..1..0..0....0..0..0..1..0..0....0..0..0..1..0..0

%e ..0..1..0..0..0..0....0..0..0..1..0..0....0..0..0..1..0..0....0..0..0..1..0..0

%e ..0..1..1..1..1..0....0..0..0..1..0..0....1..0..1..1..0..0....0..1..1..1..0..1

%e ..0..0..0..0..1..0....0..0..0..1..1..0....1..0..1..0..0..0....0..1..0..0..0..1

%e ..0..0..0..1..1..0....1..0..0..0..1..1....0..0..1..0..0..1....0..1..1..1..1..0

%e ..1..1..0..1..0..0....1..0..0..0..0..0....0..0..1..0..0..1....0..0..0..0..1..0

%e ..0..1..0..1..0..0....0..0..1..1..0..1....0..0..1..0..0..0....0..0..0..0..1..0

%Y Column 1 is A000045.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Jan 03 2011