A153284 a(n) = n + Sum_{j=1..n-1} (-1)^j * a(j) for n >= 2, a(1) = 1.

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

Offset

1,3

Comments

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; a(n)=3 if n is odd other than 1.

G.f.: x*(1 + x + 2*x^2)/((1+x)*(1-x)). - Klaus Brockhaus, Jan 04 2009 and Oct 15 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; // 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: A373403 A063062 A066056 * A112030 A010684 A176040

Adjacent sequences: A153281 A153282 A153283 * A153285 A153286 A153287

Keyword

easy,nonn

Author

Walter Carlini, Dec 23 2008

Status

approved