A241751 a(n) = n^2 + 16.
16, 17, 20, 25, 32, 41, 52, 65, 80, 97, 116, 137, 160, 185, 212, 241, 272, 305, 340, 377, 416, 457, 500, 545, 592, 641, 692, 745, 800, 857, 916, 977, 1040, 1105, 1172, 1241, 1312, 1385, 1460, 1537, 1616, 1697, 1780, 1865, 1952, 2041, 2132, 2225, 2320, 2417, 2516
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Haskell
a241751 = (+ 16) . (^ 2) -- Reinhard Zumkeller, Apr 11 2015
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Magma
[n^2+16: n in [0..60]];
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Mathematica
Table[n^2 + 16, {n, 0, 60}] -
PARI
a(n)=n^2+16 \\ Charles R Greathouse IV, Jun 17 2017
Formula
G.f.: (16 - 31*x + 17*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 + 4*Pi*coth(4*Pi))/32.
Sum_{n>=0} (-1)^n/a(n) = (1 + 4*Pi*cosech(4*Pi))/32. (End)
E.g.f.: exp(x)*(16 + x + x^2). - Elmo R. Oliveira, Nov 29 2024