OFFSET
0,2
COMMENTS
One of a family of sequences with palindromic generators.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (2*n^3 + n^2 + n + 2)/2.
G.f.: (1 -2*x +7*x^2 -6*x^3)/(1-x)^5.
E.g.f.: (2 +4*x +7*x^2 +2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019
MAPLE
a := n-> (2*n^3+n^2+n+2)/2; seq(a(n), n = 0..40); # G. C. Greubel, Aug 14 2019
MATHEMATICA
CoefficientList[Series[(1 -2x +7x^2 -6x^3)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 08 2013 *)
PROG
(Magma) [(2*n^3+n^2+n+2)/2: n in [0..40]]; // Vincenzo Librandi, Aug 08 2013
(PARI) vector(40, n, n--; (2*n^3+n^2+n+2)/2) \\ G. C. Greubel, Aug 14 2019
(Sage) [(2*n^3+n^2+n+2)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..40], n-> (2*n^3+n^2+n+2)/2); # G. C. Greubel, Aug 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 21 2003
STATUS
approved