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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..80
Crossrefs
Cf. A199832.
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)
Comments