The On-Line Encyclopedia of Integer Sequences (OEIS)

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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
(history; published version)

#4 by R. H. Hardin at Sat Jul 12 07:09:25 EDT 2014

STATUS

editing

approved

#3 by R. H. Hardin at Sat Jul 12 07:09:20 EDT 2014

LINKS

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

#2 by R. H. Hardin at Sat Jul 12 07:08:53 EDT 2014

NAME

allocated for R. H. Hardin

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

DATA

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

1,1

COMMENTS

Table starts

..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

FORMULA

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]

EXAMPLE

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

CROSSREFS

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

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Jul 12 2014

STATUS

approved

editing

#1 by R. H. Hardin at Sat Jul 12 07:03:59 EDT 2014

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved