A206452 Number of 0..5 arrays of length n avoiding the consecutive pattern 0..5.

6, 36, 216, 1296, 7776, 46655, 279924, 1679508, 10076832, 60459696, 362750400, 2176455745, 13058454546, 78349047768, 470084209776, 2820444798960, 16922306043360, 101531659804415, 609176900371944, 3654983053183896

Offset

1,1

Comments

Column 5 of A206455.

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,0,0,0,0,-1).

Formula

a(n) = 6*a(n-1) - a(n-6).

Empirical: a(n) = Sum_{i=0..floor(n/6)} ((-1)^i*6^(n-6*i)*binomial(n-5*i,i)).

g.f.: x*(6 - x^5) / (1 - 6*x + x^6). - Colin Barker, Jun 16 2018

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -1, 0, 0, 0, 0, 6]^(n-1)*[6; 36; 216; 1296; 7776; 46655])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A206455.

Sequence in context: A126634 A216128 A007275 * A215748 A000400 A238936

Adjacent sequences: A206449 A206450 A206451 * A206453 A206454 A206455

Keyword

nonn,easy,changed

Author

R. H. Hardin, Feb 07 2012

Status

approved