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.

0, 594, 9898, 67852, 293464, 955602, 2567334, 6003816, 12643728, 24534258, 44579634, 76753204, 126333064, 200161234, 306926382, 457470096, 665116704, 946026642, 1319573370, 1808743836, 2440562488, 3246538834, 4263138550

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