OFFSET
0,1
COMMENTS
1 = (5)Sum(n=0,inf.1/a(n)) = 5/6 + 5/66 + 5/176 + 5/336...; with partial sums: 5/6, 10/11, 15/16...; 1 = 1/6 + Sum(n=1,inf.,25/a(n)) = 1/6 + 25/66 + 25/176 + 25/336...+...: with partial sums 1/6, 6/11, 11/16, 16/21...(5n+1)/(5n+6)...==>1.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(0)=6, a(1)=66, a(2)=176, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 11 2015
G.f.: ( -6-48*x+4*x^2 ) / (x-1)^3. - R. J. Mathar, Nov 07 2015
EXAMPLE
6 = (1)(6), 66 = (6)(11), 176 = (11)(16), 336 = (16)(21)...
MATHEMATICA
Table[Times@@(5n+{1, 6}), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {6, 66, 176}, 40] (* Harvey P. Dale, Mar 11 2015 *)
PROG
(PARI) a(n)=(5*n+1)*(5*n+6) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 19 2003
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 25 2010
STATUS
approved