A200155 -id:A200155 - cp's OEIS frontend

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.

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, 8, 49, 66, 275, 172, 195, 18, 10, 9, 64, 107, 552, 505, 1064, 243, 52, 11, 10, 81, 158, 1029, 1248, 4005, 1742, 1209, 48, 12, 11, 100, 219, 1728, 2687, 11856, 8193, 11664, 1539

Offset: 1

R. H. Hardin, Jul 12 2014

Table starts
..2....3.....4......5......6.......7.......8........9.......10........11
..2....3.....4......5......6.......7.......8........9.......10........11
..4....9....16.....25.....36......49......64.......81......100.......121
..4....9....22.....41.....66.....107.....158......219......304.......403
..8...39...112....275....552....1029....1728.....2781.....4200......6171
..8...43...172....505...1248....2687....5220.....9385....15868.....25539
.20..195..1064...4005..11856...29813...66256...134091...252060....446193
.18..243..1742...8193..29182...85529..217336...494943..1033716...2012883
.52.1209.11664..68855.294024.1006089.2920784..7483887.17365380..37197259
.48.1539.19976.147117.754712.3011889.9995864.28810117.74285448.175024363

			Some solutions for n=7 k=4
..3....1....2....0....4....0....2....3....0....4....3....1....0....2....4....1
..1....4....0....0....0....1....1....0....3....0....3....3....2....1....0....3
..2....4....2....4....4....2....3....0....4....2....0....1....3....0....4....0
..3....2....4....0....1....2....4....4....3....3....2....4....1....2....4....1
..2....3....3....1....2....1....3....0....4....0....4....4....0....1....0....0
..1....3....1....0....1....0....1....3....0....1....1....3....2....2....2....0
..3....2....1....1....4....1....2....1....2....4....3....0....1....1....4....3

R. H. Hardin, Table of n, a(n) for n = 1..9999

Column 1 is A222955, terms 1,3,5... are A000980
Column 2 is A223743
Column 3 is A223819
Row 1 is A000027(n+1)
Row 2 is A000027(n+1)
Row 3 is A000290(n+1)
Row 4 is A200155

Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2)
n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3)
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)
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)
n=6: [order 18]
n=7: [order 16]

cp's OEIS Frontend

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.

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