

A189833


a(n) = n^2 + 8.


5



8, 9, 12, 17, 24, 33, 44, 57, 72, 89, 108, 129, 152, 177, 204, 233, 264, 297, 332, 369, 408, 449, 492, 537, 584, 633, 684, 737, 792, 849, 908, 969, 1032, 1097, 1164, 1233, 1304, 1377, 1452, 1529, 1608, 1689, 1772, 1857, 1944, 2033
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OFFSET

0,1


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000 (terms 0..955 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

From G. C. Greubel, Jan 13 2018
G.f.: (8  15*x + 9*x^2)/(1  x)^3.
E.g.f.: (8 + x + x^2)*exp(x). (End)
From Amiram Eldar, Jul 04 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + 2*sqrt(2)*Pi*coth(2*sqrt(2)*Pi))/16.
Sum_{n>=0} (1)^n/a(n) = (1 + 2*sqrt(2)*Pi*cosech(2*sqrt(2)*Pi))/16. (End)


MATHEMATICA

Table[n^2+8, {n, 0, 100}]


PROG

(MAGMA) [n^2+8: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(PARI) a(n)=n^2+8 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A002522, A059100, A117950, A087475.
Sequence in context: A264828 A080756 A304661 * A336711 A063080 A167131
Adjacent sequences: A189830 A189831 A189832 * A189834 A189835 A189836


KEYWORD

nonn,easy


AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 28 2011


EXTENSIONS

Offset changed from 1 to 0 by Vincenzo Librandi, Apr 29 2011


STATUS

approved



