OFFSET
0,2
COMMENTS
Sum of consecutive pairs of elements of A025192.
The alternating sign sequence with g.f. (1-x^2)/(1+3x) gives the diagonal sums of A110168. - Paul Barry, Jul 14 2005
Let M = an infinite lower triangular matrix with the odd integers (1,3,5,...) in every column, with the leftmost column shifted up one row. Then A080923 = lim_{n->inf} M^n. - Gary W. Adamson, Feb 18 2010
a(n+1), n >= 0, with o.g.f. ((1-x^2)/(1-3*x)-1)/x = (3-x)/(1-3*x) provides the coefficients in the formal power series for tan(3*x)/tan(x) = (3-z)/(1-3*z) = Sum_{n>=0} a(n+1)*z^n, with z = tan(x)^2. Convergence holds for 0 <= z < 1/3, i.e., |x| < Pi/6, approximately 0.5235987758. For the numerator and denominator of this o.g.f. see A034867 and A034839, respectively. - Wolfdieter Lang, Jan 18 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (3).
FORMULA
G.f.: (1-x^2)/(1-3*x).
G.f.: 1/(1 - 3*x + x^2 - 3*x^3 + x^4 - 3*x^5 + ...). - Gary W. Adamson, Jan 06 2011
a(n) = 2^3*3^(n-2), n >= 2, a(0) = 1, a(1) = 3. - Wolfdieter Lang, Jan 18 2013
MATHEMATICA
CoefficientList[Series[(1 - x^2) / (1 - 3 x), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 05 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 26 2003
STATUS
approved