The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A193643 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A193643

Number of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero
(history; published version)

#11 by R. J. Mathar at Thu Feb 19 14:44:35 EST 2015

STATUS

reviewed

approved

#10 by Joerg Arndt at Thu Feb 19 14:13:51 EST 2015

STATUS

proposed

reviewed

#9 by R. J. Mathar at Thu Feb 19 14:12:10 EST 2015

STATUS

editing

proposed

#8 by R. J. Mathar at Thu Feb 19 14:12:04 EST 2015

FORMULA

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +a(n-3).

Empirical: G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x^2+3*x-1) ). - R. J. Mathar, Feb 19 2015

Empirical: a(n)+a(n+1) = 2*A003688(n+1). - R. J. Mathar, Feb 19 2015

STATUS

approved

editing

#7 by Russ Cox at Sat Mar 31 12:36:21 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Aug 02 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875

#6 by Ron Hardin at Tue Aug 02 08:44:29 EDT 2011

STATUS

editing

approved

#5 by Ron Hardin at Tue Aug 02 08:44:25 EDT 2011

COMMENTS

Column 3 of A193648

STATUS

approved

editing

#4 by Ron Hardin at Tue Aug 02 08:35:14 EDT 2011

STATUS

editing

approved

#3 by Ron Hardin at Tue Aug 02 08:34:56 EDT 2011

LINKS

R. H. Hardin, <a href="/A193643/b193643.txt">Table of n, a(n) for n = 1..200</a>

#2 by Ron Hardin at Tue Aug 02 08:34:25 EDT 2011

NAME

allocated for Ron HardinNumber of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero

DATA

1, 7, 19, 67, 217, 721, 2377, 7855, 25939, 85675, 282961, 934561, 3086641, 10194487, 33670099, 111204787, 367284457, 1213058161, 4006458937, 13232434975, 43703763859, 144343726555, 476734943521, 1574548557121, 5200380614881

OFFSET

1,2

FORMULA

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +a(n-3)

EXAMPLE

Some solutions for n=6

..2....1...-1....0....0....0....1....0....2...-2....2....1...-3....0....0....0

.-2...-1....1...-1...-3....0...-1....3...-2....2...-2...-1....3...-2....0....0

.-1....1....2....1....3....0....1...-3....2...-3...-2...-3....1....2....2....0

..1....0...-2...-3...-1...-2....1....3....0....3....2....3...-1....0...-2...-3

.-1...-3....0....3....1....2...-1...-3...-2....0....1...-2....2....2....2....3

..0....3....0...-3....0....0....1....0....2....0...-1....2...-2...-2...-2....0

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Aug 02 2011

STATUS

approved

editing