|
| |
|
|
A027692
|
|
a(n) = n^2 + n + 7.
|
|
7
|
|
|
|
7, 9, 13, 19, 27, 37, 49, 63, 79, 97, 117, 139, 163, 189, 217, 247, 279, 313, 349, 387, 427, 469, 513, 559, 607, 657, 709, 763, 819, 877, 937, 999, 1063, 1129, 1197, 1267, 1339, 1413, 1489, 1567, 1647, 1729, 1813, 1899, 1987, 2077, 2169, 2263
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Integers k for which the discriminant of x^3-k*x-k is a square. - Jacob A. Siehler, Mar 14 2009
|
|
|
LINKS
|
Muniru A Asiru, Table of n, a(n) for n = 0..3000
Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
For n > 2: a(n) = A176271(n+1,4). - Reinhard Zumkeller, Apr 13 2010
a(n) = 2*n + a(n-1) (with a(0)=7). - Vincenzo Librandi, Aug 05 2010
G.f.: (-7 + 12*x - 7*x^2) / (x-1)^3. - R. J. Mathar, Feb 06 2011
a(n+1) = n^2+3*n+9, see A005471. - R. J. Mathar, Jun 06 2019
a(n) mod 6 = A109007(n+2). - R. J. Mathar, Jun 06 2019
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*3*sqrt(3)/2)/(3*sqrt(3)). - Amiram Eldar, Jan 17 2021
|
|
|
MAPLE
|
A027692 := proc(n)
n*(n+1)+7 ;
end proc: # R. J. Mathar, Jun 06 2019
|
|
|
MATHEMATICA
|
f[n_]:=n^2+n+7; f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)
|
|
|
PROG
|
(PARI) a(n)=n^2+n+7 \\ Charles R Greathouse IV, Jun 11 2015
(GAP) List([0..50], n->n^2+n+7); # Muniru A Asiru, Jul 15 2018
|
|
|
CROSSREFS
|
Cf. A002522, A005471 (subset of primes), A109007, A176271.
Sequence in context: A129069 A258616 A125866 * A343001 A297063 A185720
Adjacent sequences: A027689 A027690 A027691 * A027693 A027694 A027695
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Patrick De Geest
|
|
|
STATUS
|
approved
|
| |
|
|
