OFFSET
0,3
COMMENTS
The old entry with this sequence number was a duplicate of A010892.
This sequence is visible in the identity 4/Pi = 1 + 1/(3 + 4/(5 + 9/(7 + 16/(9 + 25/(11 + ...))))) (see the Wolfram Research web site).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Wolfram Research, Pi
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: (1+x^2)*(x^2-x-1)/((x-1)^3*(1+x)^3). - R. J. Mathar, Jan 05 2009
From Colin Barker, Jan 27 2016: (Start)
a(n) = (-1)*((1+n)*(-5-3*(-1)^n+(-1+(-1)^n)*n))/8.
a(n) = n-1 for n even.
a(n) = (n^2+2*n+1)/4 for n odd.
(End)
MAPLE
f:=n->if n mod 2 = 0 then n+1 else ((n+1)/2)^2; fi;
MATHEMATICA
Riffle[2 Range@ Floor[#/2] - 1, Range[#]^2] &@66 (* or *) CoefficientList[Series[(1 + x^2) (x^2 - x - 1)/((x - 1)^3*(1 + x)^3), {x, 0, 64}], x] (* Michael De Vlieger, Jan 27 2016 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 1, 3, 4, 5, 9}, 70] (* Vincenzo Librandi, Jan 28 2016 *)
PROG
(PARI) Vec((1+x^2)*(x^2-x-1)/((x-1)^3*(1+x)^3) + O(x^100)) \\ Colin Barker, Jan 27 2016
(Magma) [(-1)*((1+n)*(-5-3*(-1)^n+(-1+(-1)^n)*n))/8: n in [0..70]]; // Vincenzo Librandi, Jan 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 20 2008
STATUS
approved