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A085026
a(n) = (6*n+1)*(6*n+7).
0
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
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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 19 2003
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 25 2010
STATUS
approved