|
| |
|
|
A153284
|
|
a(n)=n+sum((-1)^(j))*a(j)); for j=1 to n-1; with a(1)=1
|
|
6
| |
|
|
1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Equals row sums of triangle A153860 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 03 2009]
1 followed by interleaving of A000012 and A010701. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
|
|
|
FORMULA
| a(n)=1 if n is 1 or even number
a(n)=3 if n is any odd number other than 1
G.f.: x*(1+x+2*x^2)/((1+x)*(1-x)). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
|
|
|
EXAMPLE
| a(1)=1, a(2)=2-a(1)=2-1=1, a(3)=3+a(2)-a(1)=3+1-1=3, a(4)=4-a(3)+a(2)-a(1)=4-3+1-1=1, a(5)=5+1-3+1-1=3,
a(6)=6-3+1-3+1-1=1, a(7)=7+1-3+1-3+1-1, etc.
|
|
|
PROG
| (MAGMA) S:=[ 1 ]; for n in [2..105] do Append(~S, n + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
|
|
|
CROSSREFS
| Equals A010684 with the addition of the leading term of 1
The first sequence of a family that includes A153285 and A153286
Cf. A153860.
Cf. A000012 (all 1's sequence), A010701 (all 3's sequence). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
Sequence in context: A102368 A063062 A066056 * A112030 A010684 A176040
Adjacent sequences: A153281 A153282 A153283 * A153285 A153286 A153287
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Walter Carlini (wgcarlini(AT)charter.net), Dec 23 2008
|
|
|
EXTENSIONS
| G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 15 2009
|
| |
|
|
