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A241849 a(n) = n^2 + 19. 2
19, 20, 23, 28, 35, 44, 55, 68, 83, 100, 119, 140, 163, 188, 215, 244, 275, 308, 343, 380, 419, 460, 503, 548, 595, 644, 695, 748, 803, 860, 919, 980, 1043, 1108, 1175, 1244, 1315, 1388, 1463, 1540, 1619, 1700, 1783, 1868, 1955, 2044, 2135, 2228, 2323 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: (19 - 37*x + 20*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(19)*Pi*coth(sqrt(19)*Pi))/38.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End)
MAPLE
A241849:=n->n^2+19: seq(A241849(n), n=0..100); # Wesley Ivan Hurt, Jan 16 2017
MATHEMATICA
Table[n^2 + 19, {n, 0, 60}]
LinearRecurrence[{3, -3, 1}, {19, 20, 23}, 50] (* Harvey P. Dale, Dec 05 2018 *)
PROG
(Magma) [n^2+19: n in [0..60]];
(PARI) a(n)=n^2+19 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. similar sequences listed in A114962.
Sequence in context: A007640 A265201 A274340 * A054304 A151979 A022109
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 01 2014
STATUS
approved

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Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)