A267227 Number of length-n 0..3 arrays with no following elements greater than or equal to the first repeated value.

4, 16, 54, 176, 564, 1790, 5646, 17732, 55512, 173354, 540258, 1680848, 5221740, 16200758, 50204790, 155413724, 480622848, 1484980802, 4584213642, 14140323560, 43583756436, 134239102286, 413179757214, 1270924525556, 3906925144104

Offset

1,1

Comments

Column 3 of A267232.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4) for n > 5.

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: 2*x*(2 - 10*x + 13*x^2 - x^3 - 3*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2).

a(n) = (-9 - 9*2^n + 11*3^(1+n) + 2*3^n*n) / 18 for n>1.

(End)

Example

Some solutions for n=6:
  2  0  1  2  3  2  1  2  3  0  3  1  1  3  2  3
  3  1  3  0  0  1  2  3  1  1  2  0  0  3  0  2
  2  0  1  2  3  3  3  0  3  0  1  2  3  0  2  3
  0  3  3  3  1  2  0  2  1  1  3  1  0  2  3  0
  3  3  2  3  1  2  1  3  2  2  2  0  1  1  1  1
  0  2  0  0  0  0  2  1  2  3  0  3  3  0  1  2

Crossrefs

Cf. A267232.

Sequence in context: A254823 A134968 A238419 * A223944 A127634 A331457

Adjacent sequences: A267224 A267225 A267226 * A267228 A267229 A267230

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved