|
| |
|
|
A001513
|
|
a(n) = (6*n+1)*(6*n+5).
|
|
2
|
|
|
|
5, 77, 221, 437, 725, 1085, 1517, 2021, 2597, 3245, 3965, 4757, 5621, 6557, 7565, 8645, 9797, 11021, 12317, 13685, 15125, 16637, 18221, 19877, 21605, 23405, 25277, 27221, 29237, 31325, 33485, 35717, 38021, 40397, 42845, 45365, 47957, 50621, 53357, 56165, 59045
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
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).
|
|
|
FORMULA
|
Sum_{k>=0} 1/a(k) = Pi/(8*sqrt(3)) = 0.22672492... - Jaume Oliver Lafont, May 30 2010
a(n) = 72*n + a(n-1) with a(0)=5. - Vincenzo Librandi, Nov 12 2010
G.f.: (-5 - 62*x - 5*x^2) / (x-1)^3. - R. J. Mathar, Jan 19 2013
From Amiram Eldar, Feb 19 2023: (Start)
a(n) = A016921(n)*A016969(n).
Sum_{n>=0} (-1)^n/a(n) = log(2+sqrt(3))/(4*sqrt(3)).
Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6).
Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/6). (End)
|
|
|
MATHEMATICA
|
a[n_] := (6*n + 1)*(6*n + 5); Array[a, 40, 0] (* Amiram Eldar, Feb 19 2023 *)
|
|
|
PROG
|
(PARI) a(n)=(6*n+1)*(6*n+5) \\ Charles R Greathouse IV, Jun 17 2017
|
|
|
CROSSREFS
|
Cf. A016921, A016969.
Sequence in context: A202607 A222533 A059856 * A028556 A214867 A330999
Adjacent sequences: A001510 A001511 A001512 * A001514 A001515 A001516
|
|
|
KEYWORD
|
nonn,easy,changed
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
