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%I #3 Mar 31 2012 12:35:49
%S 2,4,4,8,15,8,16,57,57,16,32,216,417,216,32,64,819,3032,3032,819,64,
%T 128,3105,22077,42176,22077,3105,128,256,11772,160697,587920,587920,
%U 160697,11772,256,512,44631,1169792,8191392,15701273,8191392,1169792,44631,512
%N T(n,k)=Number of nXk binary matrices with no 2X2 block having four 1's
%C Table starts
%C ....2......4.........8...........16..............32.................64
%C ....4.....15........57..........216.............819...............3105
%C ....8.....57.......417.........3032...........22077.............160697
%C ...16....216......3032........42176..........587920............8191392
%C ...32....819.....22077.......587920........15701273..........419045269
%C ...64...3105....160697......8191392.......419045269........21418970801
%C ..128..11772...1169792....114142368.....11185495872......1095020802848
%C ..256..44631...8515337...1590466304....298561305103.....55979092539545
%C ..512.169209..61986457..22161786304...7969215344753...2861765993703849
%C .1024.641520.451223152.308805072256.212714316418464.146298965997241152
%H R. H. Hardin, <a href="/A181253/b181253.txt">Table of n, a(n) for n=1..721</a>
%F Empirical column 1: a(n)=2*a(n-1)
%F Empirical column 2: a(n)=3*a(n-1)+3*a(n-2)
%F Empirical column 3: a(n)=6*a(n-1)+10*a(n-2)-5*a(n-3)
%F Empirical column 4: a(n)=10*a(n-1)+54*a(n-2)+16*a(n-3)-64*a(n-4)
%F Empirical column 5: a(n)=20*a(n-1)+188*a(n-2)-192*a(n-3)-1660*a(n-4)+2804*a(n-5)-507*a(n-6)-624*a(n-7)
%F Empirical column 6: a(n)=33*a(n-1)+908*a(n-2)+1687*a(n-3)-37947*a(n-4)-16572*a(n-5)+513993*a(n-6)-663729*a(n-7)-486540*a(n-8)+617409*a(n-9)+191835*a(n-10)-49140*a(n-11)
%F Empirical column 7: a(n)=68*a(n-1)+3106*a(n-2)-10300*a(n-3)-731184*a(n-4)+3930848*a(n-5)+47046600*a(n-6)-471525808*a(n-7)+1012118640*a(n-8)+2396096576*a(n-9)-9445394304*a(n-10)-4382776896*a(n-11)+29415041536*a(n-12)+8676097024*a(n-13)-36065068032*a(n-14)-14871987200*a(n-15)+10138337280*a(n-16)+2907136000*a(n-17)-1119682560*a(n-18)
%F Empirical column 8: a(n)=113*a(n-1)+13879*a(n-2)+91506*a(n-3)-13567062*a(n-4)-45766270*a(n-5)+5948333641*a(n-6)-25692714697*a(n-7)-932093986319*a(n-8)+9749317949468*a(n-9)+6293344318720*a(n-10)-400364584466276*a(n-11)+544975615003201*a(n-12)+8011657063605359*a(n-13)-12237642139437047*a(n-14)-98976024373360414*a(n-15)+87321080164809042*a(n-16)+743714645681446194*a(n-17)-21941742884172873*a(n-18)-2838216189512832023*a(n-19)-1559534908222727729*a(n-20)+4451110188283146640*a(n-21)+3110756142589939204*a(n-22)-3806251587192837456*a(n-23)-2258950594106495040*a(n-24)+1998716044109621760*a(n-25)+565195437997056000*a(n-26)-541032812384256000*a(n-27)+28184753405952000*a(n-28)+19493777571840000*a(n-29)
%Y Diagonal is A139810
%Y Column 2 is A125145
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Oct 10 2010
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