A200844 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases or two consecutive decreases.
512, 11235, 99700, 552247, 2276028, 7642875, 22063924, 56687801, 132734964, 288116455, 587136848, 1134248583, 2093008152, 3711583751, 6356379032, 10555568481, 17054586712, 26885876603, 41455479708, 62649346759, 92962556324
Offset: 1
Keywords
Examples
Some solutions for n=3: 1 2 1 1 3 2 3 1 1 2 2 1 3 0 3 0 1 3 1 0 2 2 3 1 0 3 1 3 3 2 2 1 0 0 3 3 3 3 2 0 2 1 3 3 1 1 3 1 0 1 2 1 2 1 3 3 0 1 0 0 3 2 3 2 3 1 2 2 2 3 3 1 1 3 3 0 3 2 0 2 1 3 2 2 0 1 3 1 0 1 1 2 2 0 0 1 2 0 3 0 1 3 0 3 2 3 3 0 3 1 0 2 1 1 0 3 1 1 2 2 0 0 3 3 3 1 2 1 3 0 2 2 2 3 0 2 1 1 2 3 0 1 1 1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = (124/2835)*n^9 + (1123/1120)*n^8 + (244/27)*n^7 + (1991/48)*n^6 + (57133/540)*n^5 + (74183/480)*n^4 + (291427/2268)*n^3 + (9739/168)*n^2 + (568/45)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(512 + 6115*x + 10390*x^2 - 618*x^3 - 622*x^4 + 36*x^5 + 94*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