OFFSET
0,2
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 2*x*(5 + 22*x + 5*x^2)/(-1 + x)^4. - Michael De Vlieger, Jan 09 2016
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3. - Colin Barker, Jan 10 2016
From Amiram Eldar, Jan 04 2022: (Start)
Sum_{n>=1} 1/a(n) = 9*log(2)/2 - 3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3 - 3*(2-sqrt(2))*log(2)/4 - 3*sqrt(2)*log(sqrt(2)+2)/2. (End)
a(n) = binomial(4*n+1, 3). - Michel Marcus, Mar 05 2022
EXAMPLE
a(4) = (32/3)*4^3 - (2/3)*4 = 680.
MATHEMATICA
Table[(32 n^3 - 2 n)/3, {n, 0, 42}] (* or *)
CoefficientList[Series[(2 x (5 + 22 x + 5 x^2))/(-1 + x)^4, {x, 0, 41}], x] (* Michael De Vlieger, Jan 09 2016 *)
PROG
(Magma) [32/3*n^3-2/3*n: n in [0..35]]; // Vincenzo Librandi, Jan 10 2016
(PARI) concat(0, Vec(2*x*(5+22*x+5*x^2)/(1-x)^4 + O(x^100))) \\ Colin Barker, Jan 10 2016
(PARI) a(n) = (32*n^3 - 2*n)/3; \\ Altug Alkan, Jan 10 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter M. Chema, Jan 09 2016
EXTENSIONS
More terms from Michael De Vlieger, Jan 09 2016
First term added from Vincenzo Librandi, Jan 10 2016
STATUS
approved