0,2

This is the m=11 member of the m-family of sequences S(n,m-2)+S(n-1,m-2) = S(2*n,sqrt(m)) (for S(n,x) see Formula). The m=4..10 instances are: A005408, A002878, A001834, A030221, A002315, A033890, and A057080, resp. The m=1..3 (signed) sequences are: A057078, A057077, and A057079, resp.

a(n) = L(n,-9)*(-1)^n, where L is defined as in A108299; see also A070998 for L(n,+9). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 01 2005

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eq.(44), rhs, m=11.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 9*a(n-1)-a(n-2), a(-1)=-1, a(0)=1.

a(n)= S(n, 9)+S(n-1, 9)= S(2*n, sqrt(11)) with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 9)= A018913(n).

G.f.: (1+x)/(1-9*x+x^2).

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then (-1)^n*q(n, -11)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002

Sequence in context: A000826 A031416 A120923 this_sequence A024132 A044261 A065690

Adjacent sequences: A057078 A057079 A057080 this_sequence A057082 A057083 A057084

nonn

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Aug 04 2000