

A117951


a(n) = n^2 + 5.


13



5, 6, 9, 14, 21, 30, 41, 54, 69, 86, 105, 126, 149, 174, 201, 230, 261, 294, 329, 366, 405, 446, 489, 534, 581, 630, 681, 734, 789, 846, 905, 966, 1029, 1094, 1161, 1230, 1301, 1374, 1449, 1526, 1605, 1686, 1769, 1854, 1941, 2030, 2121, 2214, 2309, 2406, 2505
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OFFSET

0,1


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, NearSquare Prime
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 2*n + a(n1)  1 (with a(0)=5).  Vincenzo Librandi, Nov 13 2010
From Colin Barker, Apr 10 2012: (Start)
a(n) = 3*a(n1)  3*a(n2) + a(n3).
G.f.: (59*x+6*x^2)/(1x)^3. (End)
From Amiram Eldar, Jul 13 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(5)*Pi*coth(sqrt(5)*Pi))/10.
Sum_{n>=0} (1)^n/a(n) = (1 + sqrt(5)*Pi*cosech(sqrt(5)*Pi))/10. (End)


MATHEMATICA

lst={}; Do[AppendTo[lst, n^2+5], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
Range[0, 50]^2+5 (* or *) LinearRecurrence[{3, 3, 1}, {5, 6, 9}, 60] (* Harvey P. Dale, Aug 04 2020 *)


PROG

(sage) [lucas_number1(3, n, 5) for n in range(0, 51)] # Zerinvary Lajos, May 16 2009
(PARI) a(n)=n^2+5 \\ Charles R Greathouse IV, Apr 10 2012


CROSSREFS

For numbers n such that n^2 + 5 is prime, see A078402.
Sequence in context: A301658 A286338 A344231 * A328115 A327975 A227611
Adjacent sequences: A117948 A117949 A117950 * A117952 A117953 A117954


KEYWORD

nonn,easy


AUTHOR

Eric W. Weisstein, Apr 04 2006


STATUS

approved



