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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

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Last modified April 14 15:18 EDT 2021. Contains 342949 sequences. (Running on oeis4.)