0,3

The g.f. is a Chebyshev transform of 1/(1+x-2x^2-x^3) under the Chebyshev mapping g(x)->(1/(1+x^2))g(x/(1+x^2)). The denominator is the 7th cyclotomic polynomial. The inverse of the 7 cyclotomic polynomial A014016 is given by sum{k=0..n, A099918(n-k)(k/2+1)(-1)^(k/2)(1+(-1)^k)/2}.

G.f.: (1+x^2)^2/(1+x+x^2+x^3+x^4+x^5+x^6); a(n)=sum{k=0..floor(n/2), C(n-k, k)^(-1)^k*b(n-2k)}, where b(n)=A094790(n/2+1)(1+(-1)^n)/2+A094789((n+1)/2)(1-(-1)^n)/2=(-1)^n*A006053(n+2).

Cf. A099860.

Sequence in context: A090477 A087479 A039978 this_sequence A099860 A123736 A081389

Adjacent sequences: A099915 A099916 A099917 this_sequence A099919 A099920 A099921

easy,sign

Paul Barry (pbarry(AT)wit.ie), Oct 30 2004