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+9*n^2+9*n+2)/2.
G.f.: (1+6*x-9*x^2+2*x^3)/(1-x)^5.
From Bruno Berselli, Jun 04 2010: (Start)
G.f.: (1+7*x-2*x^2)/(1-x)^4 (simplified).
a(n) = (n+1)*(2*n^2+7*n+2)/2.
a(n) -4*a(n-1) +6*a(n-2) -4*a(n-3) +a(n-4) = 0, with n>3.
E.g.f.: (1/2)*exp(x)*(2 +20*x + 15*x^2 + 2*x^3). - Stefano Spezia, Aug 15 2019
MAPLE
seq((2*n^3+9*n^2+9*n+2)/2, n=0..45); # G. C. Greubel, Aug 14 2019
MATHEMATICA
CoefficientList[Series[(1 +6x -9x^2 +2x^3)/(1-x)^5, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 11, 36, 82}, 50] (* Harvey P. Dale, Jan 20 2022 *)
PROG
(Magma) [(2*n^3+9*n^2+9*n+2)/2: n in [0..45]]; // Vincenzo Librandi, Aug 08 2013
(PARI) vector(45, n, n--; (2*n^3+9*n^2+9*n+2)/2) \\ G. C. Greubel, Aug 14 2019
(Sage) [(2*n^3+9*n^2+9*n+2)/2 for n in (0..45)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..45], n-> (2*n^3+9*n^2+9*n+2)/2); # G. C. Greubel, Aug 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 21 2003
STATUS
approved