A136016 a(n) = 9*n^2-1.
8, 35, 80, 143, 224, 323, 440, 575, 728, 899, 1088, 1295, 1520, 1763, 2024, 2303, 2600, 2915, 3248, 3599, 3968, 4355, 4760, 5183, 5624, 6083, 6560, 7055, 7568, 8099, 8648, 9215, 9800, 10403, 11024, 11663, 12320, 12995, 13688, 14399, 15128, 15875, 16640
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..3000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[9*n^2-1: n in [1..50]]; // Vincenzo Librandi, May 09 2011
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Mathematica
Table[9n^2 - 1, {n, 1, 100}] LinearRecurrence[{3,-3,1},{8,35,80},50] (* Harvey P. Dale, Oct 09 2012 *) -
PARI
a(n)=9*n^2-1 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = A005563(3*n-1). - Paul Curtz, Oct 28 2008
a(2*n) = A136017(n). - Paul Curtz, Sep 30 2008
G.f.: x*(-8-11*x+x^2) / ( x-1 )^3. - R. J. Mathar, Jul 01 2011
From Amiram Eldar, Jul 31 2020: (Start)
Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/18.
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/9 - 1/2. (End)
From Amiram Eldar, Feb 04 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = 2*Pi/(3*sqrt(3)) (A248897).
Product_{n>=1} (1 - 1/a(n)) = sqrt(2/3)*sin(sqrt(2)*Pi/3). (End)
a(n) = a(-n) for all n in Z. Sum_{n in Z} 1/a(n) = -Pi/3^(3/2) = -A073010. - Michael Somos, May 21 2023
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Jun 19 2025