A267230 Number of length-n 0..6 arrays with no following elements greater than or equal to the first repeated value.

7, 49, 315, 1981, 12327, 76237, 469623, 2884909, 17686215, 108259885, 661872471, 4042575277, 24671450343, 150466937773, 917151735159, 5587651325485, 34027698639111, 207144227712301, 1260572274312087, 7668877406965933

Offset

1,1

Comments

Column 6 of A267232.

Links

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

Formula

Empirical: a(n) = 27*a(n-1) - 301*a(n-2) + 1785*a(n-3) - 6034*a(n-4) + 11508*a(n-5) - 11304*a(n-6) + 4320*a(n-7) for n > 8.

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

G.f.: x*(7 - 140*x + 1099*x^2 - 4270*x^3 + 8428*x^4 - 7476*x^5 + 1512*x^6 + 720*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2).

a(n) = (-45*2^n - 40*3^n - 45*4^n - 72*5^n + 557*6^n + 5*2^(1 + n)*3^n*n - 72) / 360 for n>1.

(End)

Example

Some solutions for n=6:
  3  2  1  3  1  2  2  0  4  0  2  0  1  3  6  3
  6  6  0  6  2  3  3  3  5  2  4  1  5  4  5  6
  2  1  3  1  0  5  5  2  2  6  3  0  3  1  5  4
  5  3  6  3  4  6  2  5  4  4  1  4  0  4  2  2
  2  1  1  4  1  5  0  1  5  0  6  6  3  2  4  0
  3  0  6  0  1  2  4  1  2  0  6  6  1  4  0  6

Crossrefs

Cf. A267232.

Sequence in context: A357146 A133046 A200783 * A188868 A267469 A126639

Adjacent sequences: A267227 A267228 A267229 * A267231 A267232 A267233

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved