OFFSET
0,2
LINKS
Karl Dilcher and Maciej Ulas, Divisibility and Arithmetic Properties of a Class of Sparse Polynomials, arXiv:2008.13475 [math.NT], 2020. See Table 1, 2nd column, p. 3.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4).
FORMULA
Binomial transform of 1, 1, 1, -1.
G.f.: (-1 + 2*x - 2*x^2 + 2*x^3)/(2*x - 1)/(2*x^2 - 2*x + 1). - R. J. Mathar, Nov 14 2007
a(n) = 2*A038504(n) for n > 0. - R. J. Mathar, Jul 17 2009
G.f.: 1/2*(1 - 1/(2*x-1) + x*Q(0)/(1-x)), where Q(k) = 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/Q(k+1) )) (continued fraction). - Sergei N. Gladkovskii, Sep 27 2013
a(n) = Sum_{j=0..n} binomial(n, j)*(-1)^binomial(j, 3); this is the case m=3 and z=-1 of f(m,n)(z) = Sum_{j=0..n} binomial(n, j)*z^binomial(j, m). See Dilcher and Ulas. - Michel Marcus, Sep 01 2020
MATHEMATICA
Join[{1}, LinearRecurrence[{4, -6, 4}, {2, 4, 6}, 60]] (* Harvey P. Dale, Jul 07 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Oct 25 2007
EXTENSIONS
More terms from Harvey P. Dale, Jul 07 2011
STATUS
approved