OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 38*A000217(n).
a(0)=0, a(1)=38, a(2)=114, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Oct 12 2012
a(0)=0, a(n)=a(n-1) +38*n. - Vincenzo Librandi, Oct 13 2012
G.f.: 38*x/(1-x)^3. - Vincenzo Librandi, Oct 13 2012
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/19.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/19.
Product_{n>=1} (1 - 1/a(n)) = -(19/Pi)*cos(sqrt(23/19)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (19/Pi)*cos(sqrt(15/19)*Pi/2). (End)
MATHEMATICA
Table[19n(n+1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 38, 114}, 40] (* Harvey P. Dale, Oct 12 2012 *)
CoefficientList[Series[38*x/(1-x)^3, {x, 0, 100}], x] (* Vincenzo Librandi, Oct 13 2012 *)
PROG
(Magma) I:=[0, 38, 114]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 13 2012
(PARI) a(n)=19*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 16 2010
EXTENSIONS
Incorrect formulas and examples removed by R. J. Mathar, Jan 04 2011
STATUS
approved