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

1,1

Comments

Row 7 of A200838.

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)

Example

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

Crossrefs

Sequence in context: A254560 A257182 A288776 * A254475 A254768 A254504

Adjacent sequences: A200841 A200842 A200843 * A200845 A200846 A200847

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved