OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-3,1).
FORMULA
G.f.: (1-x)^2/(1-2x+3x^2-x^3).
a(n) = Sum_{k=0..n} Sum_{i=0..(2k+2)} C(2k+2,i)*Sum_{j=0..(n-k-i)} C(k+j,j)*C(j,n-k-i-j)*(-1)^(n-k-j).
a(n) = Sum_{k=0..n} binomial(n+2k,3k)*(-1)^k = Sum_{k=0..n} A109955(n,k)*(-1)^k. - Philippe Deléham, Feb 18 2012
a(n) = A000931(-3*n). - Michael Somos, Sep 18 2012
a(n) = hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27). - Peter Luschny, Nov 03 2017
EXAMPLE
G.f. = 1 - 2*x^2 - 3*x^3 + 7*x^5 + 11*x^6 + x^7 - 24*x^8 - 40*x^9 + ...
MAPLE
a := n -> hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27):
seq(simplify(a(n)), n=0..39); # Peter Luschny, Nov 03 2017
MATHEMATICA
LinearRecurrence[{2, -3, 1}, {1, 0, -2}, 50] (* Vincenzo Librandi, Feb 18 2012 *)
PROG
(PARI) x='x+O('x^50); Vec((1-x)^2/(1-2*x+3*x^2-x^3)) \\ G. C. Greubel, Jul 23 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Feb 07 2011
EXTENSIONS
More terms from Philippe Deléham, Feb 07 2012
STATUS
approved