OFFSET
0,1
LINKS
G. C. Greubel, 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) = n^3/3 - n^2 + 8n/3 + 4.
G.f.: (8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1). - Alexander R. Povolotsky, Mar 31 2008
From G. C. Greubel, Feb 23 2017: (Start)
E.g.f.: (1/3)*(12 + 6*x + x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
MATHEMATICA
CoefficientList[Series[(8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 23 2017 *)
LinearRecurrence[{4, -6, 4, -1}, {4, 6, 8, 12}, 40] (* Harvey P. Dale, Jul 23 2018 *)
PROG
(PARI) x='x+O('x^50); Vec((8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1)) \\ G. C. Greubel, Feb 23 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rolf Pleisch, Mar 17 2008
STATUS
approved