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T(n,k)=Number of length n 0..k arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope
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%I #4 Jul 12 2014 07:09:25

%S 2,3,2,4,3,4,5,4,9,4,6,5,16,9,8,7,6,25,22,39,8,8,7,36,41,112,43,20,9,

%T 8,49,66,275,172,195,18,10,9,64,107,552,505,1064,243,52,11,10,81,158,

%U 1029,1248,4005,1742,1209,48,12,11,100,219,1728,2687,11856,8193,11664,1539

%N T(n,k)=Number of length n 0..k arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope

%C Table starts

%C ..2....3.....4......5......6.......7.......8........9.......10........11

%C ..2....3.....4......5......6.......7.......8........9.......10........11

%C ..4....9....16.....25.....36......49......64.......81......100.......121

%C ..4....9....22.....41.....66.....107.....158......219......304.......403

%C ..8...39...112....275....552....1029....1728.....2781.....4200......6171

%C ..8...43...172....505...1248....2687....5220.....9385....15868.....25539

%C .20..195..1064...4005..11856...29813...66256...134091...252060....446193

%C .18..243..1742...8193..29182...85529..217336...494943..1033716...2012883

%C .52.1209.11664..68855.294024.1006089.2920784..7483887.17365380..37197259

%C .48.1539.19976.147117.754712.3011889.9995864.28810117.74285448.175024363

%H R. H. Hardin, <a href="/A245134/b245134.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) -a(n-2)

%F n=2: a(n) = 2*a(n-1) -a(n-2)

%F n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3)

%F n=4: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8)

%F n=5: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)

%F n=6: [order 18]

%F n=7: [order 16]

%e Some solutions for n=7 k=4

%e ..3....1....2....0....4....0....2....3....0....4....3....1....0....2....4....1

%e ..1....4....0....0....0....1....1....0....3....0....3....3....2....1....0....3

%e ..2....4....2....4....4....2....3....0....4....2....0....1....3....0....4....0

%e ..3....2....4....0....1....2....4....4....3....3....2....4....1....2....4....1

%e ..2....3....3....1....2....1....3....0....4....0....4....4....0....1....0....0

%e ..1....3....1....0....1....0....1....3....0....1....1....3....2....2....2....0

%e ..3....2....1....1....4....1....2....1....2....4....3....0....1....1....4....3

%Y Column 1 is A222955, terms 1,3,5... are A000980

%Y Column 2 is A223743

%Y Column 3 is A223819

%Y Row 1 is A000027(n+1)

%Y Row 2 is A000027(n+1)

%Y Row 3 is A000290(n+1)

%Y Row 4 is A200155

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 12 2014