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A241889
a(n) = n^2 + 23.
2
23, 24, 27, 32, 39, 48, 59, 72, 87, 104, 123, 144, 167, 192, 219, 248, 279, 312, 347, 384, 423, 464, 507, 552, 599, 648, 699, 752, 807, 864, 923, 984, 1047, 1112, 1179, 1248, 1319, 1392, 1467, 1544, 1623, 1704, 1787, 1872, 1959, 2048, 2139, 2232, 2327
OFFSET
0,1
FORMULA
G.f.: (23 - 45*x + 24*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 04 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(23)*Pi*coth(sqrt(23)*Pi))/46.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(23)*Pi*cosech(sqrt(23)*Pi))/46. (End)
MATHEMATICA
CoefficientList[Series[(23 - 45 x + 24 x^2)/(1 - x)^3, {x, 0, 60}], x]
Range[0, 50]^2 + 23 (* or *) LinearRecurrence[{3, -3, 1}, {23, 24, 27}, 50] (* Harvey P. Dale, May 27 2014 *)
PROG
(Magma) [n^2+23: n in [0..60]];
(PARI) a(n)=n^2+23 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. similar sequences listed in A114962.
Sequence in context: A343634 A291511 A062999 * A007638 A031332 A122470
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 01 2014
STATUS
approved