A158544 a(n) = 24*n^2 - 1.
23, 95, 215, 383, 599, 863, 1175, 1535, 1943, 2399, 2903, 3455, 4055, 4703, 5399, 6143, 6935, 7775, 8663, 9599, 10583, 11615, 12695, 13823, 14999, 16223, 17495, 18815, 20183, 21599, 23063, 24575, 26135, 27743, 29399, 31103, 32855, 34655, 36503, 38399, 40343, 42335
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
I:=[23, 95, 215]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 14 2012
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Mathematica
LinearRecurrence[{3, -3, 1}, {23, 95, 215}, 50] (* Vincenzo Librandi, Feb 14 2012 *) -
PARI
for(n=1, 40, print1(24*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 14 2012
Formula
From Vincenzo Librandi, Feb 14 2012: (Start)
G.f.: -x*(23 + 26*x - x^2)/(x - 1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 06 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)) - 1)/2. (End)
From Elmo R. Oliveira, Jan 16 2025: (Start)
E.g.f.: exp(x)*(24*x^2 + 24*x - 1) + 1.
a(n) = A140811(2*n). (End)
Extensions
Comment rewritten by R. J. Mathar, Oct 16 2009
Comments