A200435 Number of -n..n arrays x(0..7) of 8 elements with zero sum and no two or three adjacent elements summing to zero.

0, 1928, 50592, 473034, 2591502, 10217182, 32233938, 86581308, 205946004, 445471164, 892792604, 1680711318, 3002811474, 5132333154, 8444609086, 13443374616, 20791260168, 31344775440, 46194094584, 66707951618, 94583955318

Offset

1,2

Comments

Row 5 of A200430.

Links

R. H. Hardin, Table of n, a(n) for n = 1..51

Formula

Empirical: a(n) = (19328/315)*n^7 - (18373/90)*n^6 + (18602/45)*n^5 - (20887/36)*n^4 + (46687/90)*n^3 - (48359/180)*n^2 + (12499/210)*n.

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

G.f.: 2*x^2*(964 + 17584*x + 61141*x^2 + 57919*x^3 + 15963*x^4 + 1053*x^5) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

Some solutions for n=3:
..0....3....1....0....1....3....0....1....0...-1...-3....3....0...-2....0...-3
..1....2....2....1....2....2...-1....0....2....0....2....2...-3...-1...-2...-2
..0...-3...-1....2....0...-1....3....3....2...-2...-1....1....2...-1...-1...-2
..3....2....0...-1...-3....0....1....2....2...-1....0....1....0...-1....2....1
..3....0...-1....3....1...-1....1...-1...-1....2...-2...-3...-3....3....2....2
.-2...-3....2....1....3...-1....1...-3...-2....1...-2...-2...-1...-1....2...-1
.-2....1...-3...-3...-1....0...-3...-2...-2....2....3....0....2....2....0....3
.-3...-2....0...-3...-3...-2...-2....0...-1...-1....3...-2....3....1...-3....2

Crossrefs

Cf. A200430.

Sequence in context: A258841 A099482 A253337 * A252108 A220717 A162386

Adjacent sequences: A200432 A200433 A200434 * A200436 A200437 A200438

Keyword

nonn

Author

R. H. Hardin, Nov 17 2011

Status

approved