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A200433 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two or three adjacent elements summing to zero. 1
0, 212, 2232, 11008, 36952, 98052, 221984, 448224, 830160, 1437204, 2356904, 3697056, 5587816, 8183812, 11666256, 16245056, 22160928, 29687508, 39133464, 50844608, 65206008, 82644100, 103628800, 128675616, 158347760, 193258260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 3 of A200430.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = (88/5)*n^5 - (109/3)*n^4 + 44*n^3 - (107/3)*n^2 + (52/5)*n.

Conjectures from Colin Barker, May 21 2018: (Start)

G.f.: 4*x^2*(53 + 240*x + 199*x^2 + 36*x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

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

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

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

CROSSREFS

Cf. A200430.

Sequence in context: A204364 A235180 A114880 * A222950 A232671 A082828

Adjacent sequences:  A200430 A200431 A200432 * A200434 A200435 A200436

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 17 2011

STATUS

approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)