A199838 Number of -n..n arrays x(0..8) of 9 elements with zero sum and no two neighbors summing to zero.

66, 23206, 645780, 6715618, 41008804, 179213048, 622300326, 1827026482, 4719970500, 11025201168, 23740333870, 47800415256, 90973748554, 165038447302, 287293180292, 482460245532, 785043786046, 1242210635346, 1917265955424

Offset

1,1

Comments

Row 7 of A199832.

Links

R. H. Hardin, Table of n, a(n) for n = 1..80

Formula

Empirical: a(n) = (259723/2240)*n^8 - (299869/5040)*n^7 + (39757/1440)*n^6 - (8303/360)*n^5 + (31829/2880)*n^4 - (8083/720)*n^3 + (32213/5040)*n^2 - (509/420)*n.

Conjectures from Colin Barker, Mar 02 2018: (Start)

G.f.: 2*x*(33 + 11306*x + 219651*x^2 + 866735*x^3 + 937667*x^4 + 283090*x^5 + 18897*x^6 + 128*x^7) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Cf. A199832.

Sequence in context: A355470 A356688 A167778 * A188453 A278848 A110150

Adjacent sequences: A199835 A199836 A199837 * A199839 A199840 A199841

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved