|
|
A206453
|
|
Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6.
|
|
1
|
|
|
7, 49, 343, 2401, 16807, 117649, 823542, 5764787, 40353460, 282473877, 1977314738, 13841186359, 96888186864, 678216484506, 4747509626755, 33232527033825, 232627406762898, 1628389870025548, 11398715248992477, 79790909854760475
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|