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A241847 a(n) = n^2 + 17. 3
17, 18, 21, 26, 33, 42, 53, 66, 81, 98, 117, 138, 161, 186, 213, 242, 273, 306, 341, 378, 417, 458, 501, 546, 593, 642, 693, 746, 801, 858, 917, 978, 1041, 1106, 1173, 1242, 1313, 1386, 1461, 1538, 1617, 1698, 1781, 1866, 1953, 2042, 2133, 2226, 2321 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (17 - 33*x + 18*x^2)/(1 - x)^3.

a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.

From Amiram Eldar, Nov 03 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(17)*Pi*coth(sqrt(17)*Pi))/34.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(17)*Pi*cosech(sqrt(17)*Pi))/34. (End)

MATHEMATICA

Table[n^2 + 17, {n, 0, 60}]

PROG

(MAGMA) [n^2+17: n in [0..60]];

(PARI) a(n)=n^2+17 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. similar sequences listed in A114962.

Sequence in context: A296865 A188049 A098159 * A295487 A308888 A084379

Adjacent sequences:  A241844 A241845 A241846 * A241848 A241849 A241850

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, May 01 2014

STATUS

approved

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Last modified September 16 08:30 EDT 2021. Contains 347469 sequences. (Running on oeis4.)