|
%I #33 Feb 22 2023 01:47:21
%S 0,34,102,204,340,510,714,952,1224,1530,1870,2244,2652,3094,3570,4080,
%T 4624,5202,5814,6460,7140,7854,8602,9384,10200,11050,11934,12852,
%U 13804,14790,15810,16864,17952,19074,20230,21420,22644,23902,25194,26520,27880,29274
%N a(n) = 17*n*(n+1).
%H Vincenzo Librandi, <a href="/A173308/b173308.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 34*A000217(n).
%F a(0)=0, a(1)=34, a(2)=102, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: 34*x/(1-x)^3. - _Colin Barker_, Jan 25 2012
%F From _Amiram Eldar_, Feb 22 2023: (Start)
%F Sum_{n>=1} 1/a(n) = 1/17.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/17.
%F Product_{n>=1} (1 - 1/a(n)) = -(17/Pi)*cos(sqrt(21/17)*Pi/2).
%F Product_{n>=1} (1 + 1/a(n)) = (17/Pi)*cos(sqrt(13/17)*Pi/2). (End)
%t Table[17n(n+1),{n,0,40}] (* _Harvey P. Dale_, Apr 06 2011 *)
%o (PARI) a(n)=34*binomial(n+1,2) \\ _Charles R Greathouse IV_, Jan 25 2012
%o (Magma) [17*n*(n+1): n in [0..50]]; // _Vincenzo Librandi_, Aug 20 2014
%Y Cf. A000217.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Feb 16 2010
%E Incorrect formulas and examples deleted by _R. J. Mathar_, Jan 04 2011
|
