

A153284


a(n) = n + sum((1)^(j))*a(j)); for j=1 to n1; 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;
text;
internal format)



OFFSET

1,3


COMMENTS

Equals row sums of triangle A153860.  Gary W. Adamson, Jan 03 2009
1 followed by interleaving of A000012 and A010701.  Klaus Brockhaus, Jan 04 2009


LINKS

Table of n, a(n) for n=1..70.
Index entries for linear recurrences with constant coefficients, signature (0, 1).


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)*(1x)).  Klaus Brockhaus, Jan 04 2009


EXAMPLE

a(1)=1, a(2)=2a(1)=21=1, a(3)=3+a(2)a(1)=3+11=3, a(4)=4a(3)+a(2)a(1)=43+11=1, a(5)=5+13+11=3, a(6)=63+13+11=1, a(7)=7+13+13+11, etc.


PROG

(MAGMA) S:=[ 1 ]; for n in [2..105] do Append(~S, n + &+[ (1)^j*S[j]: j in [1..n1] ]); end for; S; // Klaus Brockhaus, 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).  Klaus Brockhaus, Jan 04 2009
Sequence in context: A277109 A063062 A066056 * A112030 A010684 A176040
Adjacent sequences: A153281 A153282 A153283 * A153285 A153286 A153287


KEYWORD

easy,nonn


AUTHOR

Walter Carlini, Dec 23 2008


EXTENSIONS

G.f. corrected by Klaus Brockhaus, Oct 15 2009


STATUS

approved



