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A245134 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.

%I A245134 #6 Jul 23 2025 11:28:53
%S A245134 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 A245134 8,49,66,275,172,195,18,10,9,64,107,552,505,1064,243,52,11,10,81,158,
%U A245134 1029,1248,4005,1742,1209,48,12,11,100,219,1728,2687,11856,8193,11664,1539
%N A245134 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 A245134 Table starts
%C A245134 ..2....3.....4......5......6.......7.......8........9.......10........11
%C A245134 ..2....3.....4......5......6.......7.......8........9.......10........11
%C A245134 ..4....9....16.....25.....36......49......64.......81......100.......121
%C A245134 ..4....9....22.....41.....66.....107.....158......219......304.......403
%C A245134 ..8...39...112....275....552....1029....1728.....2781.....4200......6171
%C A245134 ..8...43...172....505...1248....2687....5220.....9385....15868.....25539
%C A245134 .20..195..1064...4005..11856...29813...66256...134091...252060....446193
%C A245134 .18..243..1742...8193..29182...85529..217336...494943..1033716...2012883
%C A245134 .52.1209.11664..68855.294024.1006089.2920784..7483887.17365380..37197259
%C A245134 .48.1539.19976.147117.754712.3011889.9995864.28810117.74285448.175024363
%H A245134 R. H. Hardin, <a href="/A245134/b245134.txt">Table of n, a(n) for n = 1..9999</a>
%F A245134 Empirical for row n:
%F A245134 n=1: a(n) = 2*a(n-1) -a(n-2)
%F A245134 n=2: a(n) = 2*a(n-1) -a(n-2)
%F A245134 n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3)
%F A245134 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 A245134 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 A245134 n=6: [order 18]
%F A245134 n=7: [order 16]
%e A245134 Some solutions for n=7 k=4
%e A245134 ..3....1....2....0....4....0....2....3....0....4....3....1....0....2....4....1
%e A245134 ..1....4....0....0....0....1....1....0....3....0....3....3....2....1....0....3
%e A245134 ..2....4....2....4....4....2....3....0....4....2....0....1....3....0....4....0
%e A245134 ..3....2....4....0....1....2....4....4....3....3....2....4....1....2....4....1
%e A245134 ..2....3....3....1....2....1....3....0....4....0....4....4....0....1....0....0
%e A245134 ..1....3....1....0....1....0....1....3....0....1....1....3....2....2....2....0
%e A245134 ..3....2....1....1....4....1....2....1....2....4....3....0....1....1....4....3
%Y A245134 Column 1 is A222955, terms 1,3,5... are A000980
%Y A245134 Column 2 is A223743
%Y A245134 Column 3 is A223819
%Y A245134 Row 1 is A000027(n+1)
%Y A245134 Row 2 is A000027(n+1)
%Y A245134 Row 3 is A000290(n+1)
%Y A245134 Row 4 is A200155
%K A245134 nonn,tabl
%O A245134 1,1
%A A245134 _R. H. Hardin_, Jul 12 2014