The On-Line Encyclopedia of Integer Sequences (OEIS)

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A199531

Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.
(history; published version)

#9 by Susanna Cuyler at Tue May 15 20:43:35 EDT 2018

STATUS

proposed

approved

#8 by Colin Barker at Tue May 15 13:48:03 EDT 2018

STATUS

editing

proposed

#7 by Colin Barker at Tue May 15 13:39:23 EDT 2018

NAME

Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.

#6 by Colin Barker at Tue May 15 13:38:26 EDT 2018

COMMENTS

Row 4 of A199530.

FORMULA

Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n.

Conjectures from Colin Barker, May 15 2018: (Start)

G.f.: 4*x*(3 + 6*x - x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

EXAMPLE

Some solutions for n=5:

CROSSREFS

Cf. A199530.

AUTHOR

R. H. Hardin , Nov 07 2011

STATUS

approved

editing

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

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Nov 07 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Mon Nov 07 20:27:05 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Mon Nov 07 20:27:02 EST 2011

LINKS

R. H. Hardin, <a href="/A199531/b199531.txt">Table of n, a(n) for n = 1..200</a>

#2 by Ron Hardin at Mon Nov 07 20:26:37 EST 2011

NAME

allocated for Ron HardinNumber of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements

DATA

12, 72, 212, 464, 860, 1432, 2212, 3232, 4524, 6120, 8052, 10352, 13052, 16184, 19780, 23872, 28492, 33672, 39444, 45840, 52892, 60632, 69092, 78304, 88300, 99112, 110772, 123312, 136764, 151160, 166532, 182912, 200332, 218824, 238420, 259152

OFFSET

1,1

COMMENTS

Row 4 of A199530

FORMULA

Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n

EXAMPLE

Some solutions for n=5

.-4...-4....4....0...-5....5....2....0...-1...-3....2....1....4...-1....4...-1

..4....5...-4....2....3...-2...-2...-2....0...-2...-2...-3...-1....2...-2....5

..3....1...-2...-5...-3...-1....1....1...-2....2....3....1....0....4....1....1

.-3...-2....2....3....5...-2...-1....1....3....3...-3....1...-3...-5...-3...-5

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Nov 07 2011

STATUS

approved

editing

#1 by Ron Hardin at Mon Nov 07 20:18:57 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved