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A200434 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two or three adjacent elements summing to zero. 1
0, 594, 9898, 67852, 293464, 955602, 2567334, 6003816, 12643728, 24534258, 44579634, 76753204, 126333064, 200161234, 306926382, 457470096, 665116704, 946026642, 1319573370, 1808743836, 2440562488, 3246538834, 4263138550 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 4 of A200430.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..144

FORMULA

Empirical: a(n) = (5887/180)*n^6 - (5813/60)*n^5 + (6083/36)*n^4 - (2191/12)*n^3 + (9119/90)*n^2 - (353/15)*n.

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

G.f.: 2*x^2*(297 + 2870*x + 5520*x^2 + 2784*x^3 + 303*x^4) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

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

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

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

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

CROSSREFS

Cf. A200430.

Sequence in context: A025330 A035138 A206211 * A241876 A252534 A249705

Adjacent sequences:  A200431 A200432 A200433 * A200435 A200436 A200437

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 17 2011

STATUS

approved

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Last modified January 22 16:49 EST 2022. Contains 350484 sequences. (Running on oeis4.)