0,2

A Pellian sequence.

In general, sum{k=0..n, binomial(2n-k,k)j^(n-k)}=(-1)^n*U(2n,I*sqrt(j)/2), I=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Mar 13 2005

a(n) = L(n,9), where L is defined as in A108299; see also A057081 for L(n,-9). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

Number of 01-avoiding words of length n on alphabet {0,1,2,3,4,5,6,7,8} which do not end in 0. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 10 2007

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

a(n) ~ 1/11*sqrt(11)*(1/2*(sqrt(11)+sqrt(7)))^(2*n+1)

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then q(n, 7)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002

a(n)a(n+3) = 63 + a(n+1)a(n+2). - R. Stephan, May 29 2004

a(n)=(-1)^n*U(2n, I*sqrt(7)/2), U(n, x) Chebyshev polynomial of second kind, I=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Mar 13 2005

G.f.: (1-x)/1-9*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]

a(n)=(1/2)*[(9/2)+(1/2)*sqrt(77)]^(n+1)+(1/22)*[(9/2)-(1/2)*sqrt(77)]^(n+1)*sqrt(77)-(1/22)*[(9/2)+(1/2) *sqrt(77)]^(n+1)*sqrt(77)+(1/2)*[(9/2)-(1/2)*sqrt(77)]^(n+1), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 2008]

(Other) sage: [lucas_number1(n, 9, 1)-lucas_number1(n-1, 9, 1) for n in xrange(1, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]

Cf. A057081, A056918.

Row 9 of array A094954.

Sequence in context: A003364 A038145 A015576 this_sequence A152265 A081178 A096341

Adjacent sequences: A070995 A070996 A070997 this_sequence A070999 A071000 A071001

nonn,new

Joe Keane (jgk(AT)jgk.org), May 18 2002