OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 8*(x^3 + 60*x^2 + 93*x + 8)/(1-x)^4. - Vincenzo Librandi, Jan 27 2013
Sum_{n>=0} 1/a(n) = -Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - Amiram Eldar, Oct 02 2020
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020
EXAMPLE
a(0) = (6*0 + 4)^3 = 4^3 = 64.
MATHEMATICA
CoefficientList[Series[8*(x^3 + 60*x^2 + 93*x + 8)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)
(6*Range[0, 30]+4)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {64, 1000, 4096, 10648}, 30] (* Harvey P. Dale, Nov 22 2018 *)
PROG
(Magma) [(6*n+4)^3: n in [0..40]]; // Vincenzo Librandi, May 06 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved