A200877 Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors or less than both neighbors.
110, 1523, 9858, 42479, 141688, 395929, 971416, 2156867, 4424298, 8509105, 15512938, 27033149, 45322876, 73486107, 115712352, 177555837, 266264422, 391163735, 564102306, 799963779, 1117252576, 1538759685, 2092315544
Offset: 1
Keywords
Examples
Some solutions for n=3 ..3....3....3....3....3....0....2....2....3....2....3....3....1....1....2....2 ..0....0....0....1....3....0....2....2....3....3....3....1....2....1....2....0 ..0....0....0....1....3....2....1....0....3....3....3....1....2....1....1....0 ..0....2....1....1....2....2....0....0....2....3....3....1....3....3....1....0 ..3....2....3....1....1....2....0....2....2....3....1....3....3....3....0....0 ..3....1....3....3....1....2....1....2....1....2....1....3....3....2....0....0 ..3....0....3....3....0....2....2....0....1....0....1....3....2....1....0....0 ..2....0....2....2....0....1....3....0....1....0....1....3....2....0....1....0 ..0....1....2....1....2....1....3....2....1....1....3....2....3....0....3....3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = (1/181440)*n^9 + (131/20160)*n^8 + (8893/30240)*n^7 + (4621/1440)*n^6 + (118933/8640)*n^5 + (83957/2880)*n^4 + (763489/22680)*n^3 + (36343/1680)*n^2 + (9169/1260)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(110 + 423*x - 422*x^2 - 766*x^3 + 848*x^4 - 246*x^5 + 90*x^6 - 44*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)
Comments