OFFSET
0,3
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
G.f.: (1-2*x+2*x^2)/((1-x^2)*(1-x)^2).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
a(n) = 5*(-1)^n/8 + (2*n^2+3)/8.
a(n) = A004652(n+1) - A004526(n+1) = ceiling(((n+1)/2)^2) - floor((n+1)/2). - Ridouane Oudra, Jun 22 2019
E.g.f.: ((4+x+x^2)*cosh(x) - (1-x-x^2)*sinh(x))/4. - G. C. Greubel, Jun 30 2019
MATHEMATICA
CoefficientList[Series[(1-2x+2x^2)/((1+x)(1-x)^3), {x, 0, 70}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 0, 2, 2}, 70] (* Harvey P. Dale, Apr 08 2014 *)
Table[(2n^2 +3 +5(-1)^n)/8, {n, 0, 70}] (* Vincenzo Librandi, Apr 09 2014 *)
PROG
(PARI) vector(70, n, n--; (2*n^2 +3 +5*(-1)^n)/8) \\ G. C. Greubel, Jun 30 2019
(Magma) [(2*n^2 +3 +5*(-1)^n)/8: n in [0..70]]; // G. C. Greubel, Jun 30 2019
(Sage) [(2*n^2 +3 +5*(-1)^n)/8 for n in (0..70)] # G. C. Greubel, Jun 30 2019
(GAP) List([0..70], n-> (2*n^2 +3 +5*(-1)^n)/8) # G. C. Greubel, Jun 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jul 22 2004
STATUS
approved