A001526 a(n) = (7*n+1)*(7*n+6).
6, 104, 300, 594, 986, 1476, 2064, 2750, 3534, 4416, 5396, 6474, 7650, 8924, 10296, 11766, 13334, 15000, 16764, 18626, 20586, 22644, 24800, 27054, 29406, 31856, 34404, 37050, 39794, 42636, 45576, 48614, 51750, 54984, 58316, 61746, 65274, 68900, 72624, 76446
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Mathematica
a[n_] := (7*n + 1)*(7*n + 6); Array[a, 40, 0] (* Amiram Eldar, Feb 19 2023 *)
-
PARI
a(n)=(7*n+1)*(7*n+6) \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 98*n + a(n-1) with a(0)=6. - Vincenzo Librandi, Nov 12 2010
From Amiram Eldar, Feb 19 2023: (Start)
Sum_{n>=0} 1/a(n) = cot(Pi/7)*Pi/35 = 0.186388....
Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/7)*cos(sqrt(29)*Pi/14).
Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/7)*cos(sqrt(3/7)*Pi/2). (End)
G.f.: -2*(3+43*x+3*x^2)/(x-1)^3. - R. J. Mathar, Apr 23 2024
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: exp(x)*(6 + 49*x*(2 + x)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)