OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 2*n^3 - 3*n^2 + 4*n - 2.
From Elmo R. Oliveira, Aug 28 2025: (Start)
G.f.: x*(1 + 6*x + 3*x^2 + 2*x^3)/(1-x)^4.
E.g.f.: 2 + exp(x)*(-2 + 3*x + 3*x^2 + 2*x^3).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)
MATHEMATICA
lst={}; Do[s0=n^3; s1=(n+1)^3; AppendTo[lst, (s1+s0)+n], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 19 2009 *)
PROG
(PARI) vector(50, n, 2*n^3 - 3*n^2 + 4*n - 2) \\ Michel Marcus, Jan 07 2015
(PARI) my(x='x+O('x^42)); Vec(x*(1+6*x+3*x^2+2*x^3)/(x-1)^4) \\ Elmo R. Oliveira, Aug 28 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Elmo R. Oliveira, Aug 28 2025
STATUS
approved