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A200844 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases or two consecutive decreases. 1
512, 11235, 99700, 552247, 2276028, 7642875, 22063924, 56687801, 132734964, 288116455, 587136848, 1134248583, 2093008152, 3711583751, 6356379032, 10555568481, 17054586712, 26885876603, 41455479708, 62649346759, 92962556324 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)