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