A206453 Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6.

7, 49, 343, 2401, 16807, 117649, 823542, 5764787, 40353460, 282473877, 1977314738, 13841186359, 96888186864, 678216484506, 4747509626755, 33232527033825, 232627406762898, 1628389870025548, 11398715248992477, 79790909854760475

Offset: 1

Author

R. H. Hardin, Feb 07 2012

Keywords

• nonn

Comments

Column 6 of A206455.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (7,0,0,0,0,0,-1).

Crossrefs

Cf. A206455.

Formula

a(n) = 7*a(n-1) - a(n-7).

Empirical: a(n) = Sum_{i=0..floor(n/7)} ((-1)^i*7^(n-7*i)*binomial(n-6*i,i)).

g.f.: x*(7 - x^6) / (1 - 7*x + x^7). - Colin Barker, Jun 16 2018