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%I #9 Sep 01 2013 17:48:59
%S 1,1,1,2,2,2,3,4,4,3,5,9,14,9,5,8,19,41,41,19,8,13,41,127,172,127,41,
%T 13,21,88,386,728,728,386,88,21,34,189,1181,3084,4354,3084,1181,189,
%U 34,55,406,3605,13050,25699,25699,13050,3605,406,55,89,872,11013,55252,152373
%N T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.
%C Table starts
%C ..1...1.....2......3.......5.........8.........13..........21............34
%C ..1...2.....4......9......19........41.........88.........189...........406
%C ..2...4....14.....41.....127.......386.......1181........3605.........11013
%C ..3...9....41....172.....728......3084......13050.......55252........233875
%C ..5..19...127....728....4354.....25699.....152373......902042.......5342712
%C ..8..41...386...3084...25699....211588....1748684....14433982.....119188751
%C .13..88..1181..13050..152373...1748684...20185842...232542935....2680777055
%C .21.189..3605..55252..902042..14433982..232542935..3737615288...60122232373
%C .34.406.11013.233875.5342712.119188751.2680777055.60122232373.1349721589622
%C Same recurrences as A228285 except in addition this smaller one for k=5
%H R. H. Hardin, <a href="/A228482/b228482.txt">Table of n, a(n) for n = 1..1333</a>
%F Recurrences for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F k=3: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) -a(n-5)
%F k=4: a(n) = a(n-1) +10*a(n-2) +15*a(n-3) +4*a(n-4) -6*a(n-5) -a(n-6) +3*a(n-7) -a(n-8)
%F k=5: a(n) = 3*a(n-1) +15*a(n-2) +16*a(n-3) -11*a(n-4) -20*a(n-5) +19*a(n-6) -8*a(n-7) +a(n-9)
%F k=6: a(n) = a(n-1) +42*a(n-2) +147*a(n-3) +70*a(n-4) -478*a(n-5) -449*a(n-6) +1199*a(n-7) +732*a(n-8) -2727*a(n-9) +659*a(n-10) +3827*a(n-11) -5776*a(n-12) +3926*a(n-13) -1152*a(n-14) -148*a(n-15) +154*a(n-16) +32*a(n-17) -29*a(n-18) -6*a(n-19) +3*a(n-20) +a(n-21)
%F k=7: a(n) = a(n-1) +85*a(n-2) +432*a(n-3) +192*a(n-4) -3711*a(n-5) -5096*a(n-6) +21164*a(n-7) +27340*a(n-8) -112654*a(n-9) -37244*a(n-10) +477721*a(n-11) -464722*a(n-12) -897815*a(n-13) +3102284*a(n-14) -4149918*a(n-15) +2761082*a(n-16) -138325*a(n-17) -1353257*a(n-18) +942033*a(n-19) +64683*a(n-20) -365483*a(n-21) +80904*a(n-22) +92350*a(n-23) -27097*a(n-24) -23292*a(n-25) +2585*a(n-26) +5635*a(n-27) +1405*a(n-28) -561*a(n-29) -545*a(n-30) -173*a(n-31) -14*a(n-32) +5*a(n-33) +a(n-34)
%e Some solutions for n=4 k=4
%e ..1..0..0..1....1..0..1..0....1..0..0..1....1..0..1..0....1..0..1..0
%e ..0..0..0..0....0..0..0..1....0..1..0..0....0..0..0..0....0..0..0..0
%e ..0..0..0..1....0..0..0..0....0..0..1..0....0..1..0..0....0..0..0..0
%e ..0..0..0..0....0..1..0..0....0..0..0..1....0..0..1..0....1..0..0..0
%Y Column 1 is A000045
%Y Column 2 is A078039(n-1).
%Y Cf. A228476-A228481, A228277-A228285, A226444.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_ Aug 22 2013
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