A085026 a(n) = (6*n+1)*(6*n+7).

7, 91, 247, 475, 775, 1147, 1591, 2107, 2695, 3355, 4087, 4891, 5767, 6715, 7735, 8827, 9991, 11227, 12535, 13915, 15367, 16891, 18487, 20155, 21895, 23707, 25591, 27547, 29575, 31675, 33847, 36091, 38407, 40795, 43255, 45787, 48391, 51067, 53815, 56635

Offset

0,1

Comments

1 = (6)Sum(n=0,inf.,1/a(n)) = 6/7 + 6/91, + 6/247 + 6/475...+...; with partial sums: 6/7, 12/13, 18/19...; 1 = 1/7 + Sum(n=1,inf.,36/a(n)) = 1/7 + 36/91 + 36/247 + 36/475...+...; with partial sums: 1/7, 7/13, 13/19, 19/25...(6n+1)/(6n+7)...==>1

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: (7+70*x-5*x^2)/(1-x)^3. - Colin Barker, Oct 28 2012

Example

7 = (1)(7), 91 = (7)(13), 247 = (13)(19), 475 = (19)(25), 775 = (25)(31)...

Prog

(PARI) a(n)=(6*n+1)*(6*n+7) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A266236 A123694 A319978 * A221132 A181475 A374094

Adjacent sequences: A085023 A085024 A085025 * A085027 A085028 A085029

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 19 2003

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010

Status

approved