A158559 a(n) = 225*n^2 - 15.
210, 885, 2010, 3585, 5610, 8085, 11010, 14385, 18210, 22485, 27210, 32385, 38010, 44085, 50610, 57585, 65010, 72885, 81210, 89985, 99210, 108885, 119010, 129585, 140610, 152085, 164010, 176385, 189210, 202485, 216210, 230385, 245010, 260085, 275610, 291585, 308010
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:=[210, 885, 2010]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
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Mathematica
15(15Range[40]^2-1) (* or *) LinearRecurrence[{3,-3,1},{210,885,2010},40] (* Harvey P. Dale, Jan 24 2012 *) -
PARI
for(n=1, 40, print1(225*n^2 - 15", ")); \\ Vincenzo Librandi, Feb 05 2012
Formula
G.f.: 15*x*(-14 - 17*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 09 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(15))*Pi/sqrt(15))/30.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(15))*Pi/sqrt(15) - 1)/30. (End)
Extensions
Comment rewritten by R. J. Mathar, Oct 16 2009
Comments