OFFSET
0,2
LINKS
Delbert L. Johnson, Table of n, a(n) for n = 0..19999
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From Jaume Oliver Lafont, Oct 20 2009: (Start)
G.f.: (1+x)*(1+30*x+x^2)/(1-x)^4.
Sum_{n>=0} 1/a(n) = (3/2)*log(2). (End)
From Ant King, Oct 19 2012: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = 64 + 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = A000292(4*n+1). - L. Edson Jeffery, Jan 16 2013
a(n) = A000447(2*n+1). - Michel Marcus, Jan 25 2016
Sum_{n>=0} (-1)^n/a(n) = 3*(sqrt(2)-1)*Pi/4. - Amiram Eldar, Jan 04 2022
a(n) = A001505(n)/6. - R. J. Mathar, Apr 17 2024
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {1, 35, 165, 455}, 35] (* Ant King, Oct 19 2012 *)
Table[(4 n + 1) (4 n + 2) (4 n + 3)/6, {n, 0, 40}] (* Vincenzo Librandi, Jan 25 2016 *)
PROG
(PARI) a(n)=binomial(4*n+3, 3) \\ Charles R Greathouse IV, Jan 16 2013
(Magma) [(4*n+1)*(4*n+2)*(4*n+3)/6: n in [0..40]]; // Vincenzo Librandi, Jan 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Erich Friedman.
STATUS
approved