OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).
FORMULA
From R. J. Mathar, Nov 04 2008: (Start)
G.f.: (1-x+x^2)/((1-x)^3*(1+x)^2*(1+x^2)). (End)
a(n) = floor((n^2 + 5*n + 13 + 3*(n+1)*(-1)^n)/16). - Tani Akinari, Aug 23 2013
a(n) = Sum_{i=1..floor((n+4)/2)} floor((i-(n mod 2))/2). - Wesley Ivan Hurt, Mar 31 2014
a(n) = (2*n^2+10*n+13+3*(2*n+5)*(-1)^n+4*(-1)^((6*n-1+(-1)^n)/4))/32. - Luce ETIENNE, Jun 09 2015
MATHEMATICA
CoefficientList[Series[(1+x^3)/((1-x^2)^2*(1-x^4)), {x, 0, 70}], x] (* Vincenzo Librandi, Aug 24 2013 *)
LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {1, 0, 2, 1, 4, 2, 6}, 70] (* Harvey P. Dale, Nov 23 2015 *)
PROG
(Magma) [Floor((n^2+5*n+13+3*(n+1)*(-1)^n)/16): n in [0..70]]; // Vincenzo Librandi, Aug 24 2013
(PARI) a(n)=((n^2+5*n+13+3*(n+1)*(-1)^n))\16 \\ Charles R Greathouse IV, Jun 11 2015
(Sage) [floor((n^2 + 5*n + 13 + 3*(n+1)*(-1)^n)/16) for n in (0..70)] # G. C. Greubel, Jul 30 2019
(GAP) List([0..70], n-> Int((n^2 + 5*n + 13 + 3*(n+1)*(-1)^n)/16)); # G. C. Greubel, Jul 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved