0,2

Number of (s(0), s(1), ..., s(2n+4)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+4, s(0) = 1, s(2n+4) = 5. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 14 2004

Binomial transform of A002878 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 04 2005

A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=5, q=-5.

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs. (38) and (45), lhs, m=5.

Index entries for sequences related to linear recurrences with constant coefficients

Index entries for sequences related to Chebyshev polynomials.

a(n)=(sqrt(5))^n*U(n, sqrt(5)/2), g.f.: 1/(5*(x^2-x+1/5)), a(2*k+1)=5^(k+1)*F(2*k+2), F(n) = Fibonacci (A000045), a(2*k)=5^k*L(2*k+1), L(n) = Lucas (A000032)

a(n-1)=sum(k=0, n, C(n, k)*F(2*k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2003

a(n) = 5*a(n-1)-5*a(n-2). - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2003

a(n-1)=((5/2+sqrt(5)/2)^n-(5/2-sqrt(5)/2)^n)/sqrt(5) is the 2nd binomial transform of Fib(n), the first binomial transform of Fib(2n) and its n-th term is the n-th term of the third binomial transform of Fib(3n) divided by 2^n. - Paul Barry (pbarry(AT)wit.ie), Mar 23 2004

a(n)=Sum_{k, 0<=k<=n}5^k*A109466(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2006

a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*5^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]

(Other) sage: [lucas_number1(n, 5, 5) for n in xrange(1, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Sequence in context: A022633 A092490 A094828 this_sequence A093131 A000344 A061278

Adjacent sequences: A030188 A030189 A030190 this_sequence A030192 A030193 A030194

nonn

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