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%I #4 Aug 04 2014 07:30:56
%S 1,1,1,1,1,2,1,1,2,2,1,1,2,2,4,1,1,2,2,5,4,1,1,2,2,5,5,8,1,1,2,2,5,5,
%T 14,8,1,1,2,2,5,5,15,16,20,1,1,2,2,5,5,15,17,65,18,1,1,2,2,5,5,15,17,
%U 77,77,52,1,1,2,2,5,5,15,17,78,101,356,48,1,1,2,2,5,5,15,17,78,102,551,448,152
%N T(n,k)=Number of length n 0..k arrays with new values introduced in order from both ends, and least squares fitting to a straight line with slope zero, with a single point taken as having zero slope
%C Table starts
%C ....1......1.......1.......1.......1.......1.......1.......1.......1.......1
%C ....1......1.......1.......1.......1.......1.......1.......1.......1.......1
%C ....2......2.......2.......2.......2.......2.......2.......2.......2.......2
%C ....2......2.......2.......2.......2.......2.......2.......2.......2.......2
%C ....4......5.......5.......5.......5.......5.......5.......5.......5.......5
%C ....4......5.......5.......5.......5.......5.......5.......5.......5.......5
%C ....8.....14......15......15......15......15......15......15......15......15
%C ....8.....16......17......17......17......17......17......17......17......17
%C ...20.....65......77......78......78......78......78......78......78......78
%C ...18.....77.....101.....102.....102.....102.....102.....102.....102.....102
%C ...52....356.....551.....568.....569.....569.....569.....569.....569.....569
%C ...48....448.....861.....918.....919.....919.....919.....919.....919.....919
%C ..152...2279....5433....6115....6142....6143....6143....6143....6143....6143
%C ..138...2959....9055...11063...11170...11171...11171...11171...11171...11171
%C ..472..15572...61725...84095...86043...86081...86082...86082...86082...86082
%C ..428..20762..107467..167139..174957..175169..175170..175170..175170..175170
%C .1520.111641..758905.1377562.1495234.1500038.1500088.1500089.1500089.1500089
%C .1392.151205.1355573.2919818.3338570.3364000.3364342.3364343.3364343.3364343
%H R. H. Hardin, <a href="/A245851/b245851.txt">Table of n, a(n) for n = 1..1121</a>
%e Some solutions for n=12 k=4
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....1....1....1....1....1....1....0....1....1....0....1....1....1....1....0
%e ..1....1....0....0....2....1....2....1....0....2....1....2....0....2....0....1
%e ..2....0....0....0....1....2....3....1....2....1....1....2....0....2....2....1
%e ..0....2....1....1....1....2....1....2....3....3....2....3....0....1....2....1
%e ..1....3....2....2....3....3....3....0....2....1....3....2....1....1....0....0
%e ..0....2....0....1....2....0....0....1....3....2....2....3....2....2....0....0
%e ..2....0....0....2....3....3....2....1....2....1....0....1....1....3....2....1
%e ..1....0....1....0....0....2....3....1....1....2....2....3....1....2....2....1
%e ..1....2....0....1....2....1....2....0....1....2....0....2....0....1....0....1
%e ..0....1....1....0....1....1....1....1....1....1....1....1....0....1....1....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y Column 1 is A222955(n-2)
%K nonn,tabl
%O 1,6
%A _R. H. Hardin_, Aug 04 2014