OFFSET
1,3
COMMENTS
From Paul Curtz, Feb 09 2015: (Start)
The nonnegative numbers with 0 instead of 1. See A254667(n), which is linked to the Bernoulli numbers A164555(n)/A027642(n), an autosequence of the second kind.
Offset 0 could be chosen.
An autosequence of the second kind is a sequence whose main diagonal is the first upper diagonal multiplied by 2. If the first upper diagonal is
s0, s1, s2, s3, s4, s5, ...,
the sequence is
Ssk(n) = 2*s0, s0, s0 + 2*s1, s0 +3*s1, s0 + 4*s1 + 2*s2, s1 + 5*s1 + 5*s2, etc.
The binomial transform of Ssk(n) is (-1)^n*Ssk(n).
Difference table of a(n):
0, 0, 2, 3, 4, 5, 6, 7, ...
0, 2, 1, 1, 1, 1, 1, ...
2, -1, 0, 0, 0, 0 ...
-3, 1, 0, 0, 0, ...
4, -1, 0, 0, ...
-5, 1, 0, ...
6, -1, ...
7, ...
etc.
a(n) is an autosequence of the second kind. See A054977(n).
The corresponding autosequence of the first kind (a companion) is 0, 0 followed by the nonnegative numbers (A001477(n)). Not in the OEIS.
Ssk(n) = 2*Sfk(n+1) - Sfk(n) where Sfk(n) is the corresponding sequence of the first kind (see A254667(n)).
(End)
Number of binary sequences of length n-1 that contain exactly one 0 and at least one 1. - Enrique Navarrete, May 11 2021
LINKS
FORMULA
a(n) = n-1 for n >= 3.
E.g.f.: 1-x^2/2+(x-1)*exp(x). - Enrique Navarrete, May 11 2021
MATHEMATICA
Join[{0, 0}, Table[Max[Complement[Range[n], Divisors[n]]], {n, 3, 70}]] (* or *) Join[{0, 0}, Range[2, 70]] (* Harvey P. Dale, May 31 2014 *)
PROG
(PARI) if(n>2, n-1, 0) \\ Charles R Greathouse IV, Sep 02 2015
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Jaroslav Krizek, Nov 26 2011
STATUS
approved