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A085025
a(n) = (5*n+1)*(5*n+6).
0
6, 66, 176, 336, 546, 806, 1116, 1476, 1886, 2346, 2856, 3416, 4026, 4686, 5396, 6156, 6966, 7826, 8736, 9696, 10706, 11766, 12876, 14036, 15246, 16506, 17816, 19176, 20586, 22046, 23556, 25116, 26726, 28386, 30096, 31856, 33666, 35526, 37436, 39396
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.
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
Sequence in context: A292456 A292736 A119140 * A048537 A133424 A045641
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 19 2003
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 25 2010
STATUS
approved