OFFSET
1,1
COMMENTS
Also obtained from A135370 if adjacent pairs are swapped and if the sequence is then multiplied by (-1)^(n+1).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-1,2,2,-1,-1).
FORMULA
a(n) = -a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5). - R. J. Mathar, Sep 12 2010
a(2n-1)+a(2n) = A005843(n).
G.f.: x(3+2x+6x^2-x^4)/((1+x)^3*(1-x)^2). - R. J. Mathar, Oct 24 2008, parenthesis added Sep 12 2010
From Colin Barker, Jan 26 2016: (Start)
a(n) = (5+3*(-1)^n+(10-6*(-1)^n)*n-6*(-1)^n*n^2)/8.
a(n) = (-3*n^2+2*n+4)/4 for n even.
a(n) = (3*n^2+8*n+1)/4 for n odd.
(End)
MATHEMATICA
CoefficientList[Series[(3 + 2 x + 6 x^2 - x^4)/((1 + x)^3 (1 - x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, May 25 2014 *)
LinearRecurrence[{-1, 2, 2, -1, -1}, {3, -1, 13, -9, 29}, 50] (* Harvey P. Dale, Apr 02 2018 *)
PROG
(PARI) Vec(x*(3+2*x+6*x^2-x^4)/((1+x)^3*(1-x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Sep 29 2008
EXTENSIONS
Edited by R. J. Mathar, Oct 24 2008
More terms from Vincenzo Librandi, May 25 2014
STATUS
approved