cp's OEIS Frontend

A124011 Add three, add six, add nine, ....

%I A124011 #53 Feb 18 2025 15:36:45
%S A124011 5,8,14,23,35,50,68,89,113,140,170,203,239,278,320,365,413,464,518,
%T A124011 575,635,698,764,833,905,980,1058,1139,1223,1310,1400,1493,1589,1688,
%U A124011 1790,1895,2003,2114,2228,2345,2465,2588,2714,2843,2975,3110,3248,3389,3533,3680
%N A124011 Add three, add six, add nine, ....
%C A124011 Found on a quiz.
%H A124011 Vincenzo Librandi, <a href="/A124011/b124011.txt">Table of n, a(n) for n = 1..1000</a>
%H A124011 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A124011 a(n) = 3*n*(n-1)/2 + 5 = 3*A000217(n-1) + 5 = A045943(n) + 5.
%F A124011 a(n) = 3*n + a(n-1) - 3 with a(1)=5. - _Vincenzo Librandi_, Nov 28 2009
%F A124011 G.f.: x*(5 - 7*x + 5*x^2)/(1-x)^3. - _Colin Barker_, Jan 14 2012
%F A124011 3*(8*a(n) - 37) = A016945(n-1)^2. - _Vincenzo Librandi_, Feb 15 2012
%F A124011 From _Elmo R. Oliveira_, Feb 11 2025: (Start)
%F A124011 E.g.f.: exp(x)*(5 + 3*x^2/2) - 5.
%F A124011 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A124011 LinearRecurrence[{3,-3,1},{5,8,14},50] (* _Vincenzo Librandi_, Feb 15 2012 *)
%t A124011 Table[(3x^2-3x+10)/2,{x,50}] (* _Harvey P. Dale_, Jul 25 2019 *)
%t A124011 Accumulate[3*Range[0,50]]+5 (* _Harvey P. Dale_, Jan 16 2024 *)
%o A124011 (Magma) I:=[5,8,14]; [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 15 2012
%o A124011 (PARI) a(n)=3*n*(n-1)/2+5 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A124011 Cf. A000217, A016945, A045943.
%K A124011 nonn,easy
%O A124011 1,1
%A A124011 Ruben Fritzon (ruben.fritzon(AT)edu.ovanaker.se), Dec 11 2006
%E A124011 More terms from Graham Roy (groy(AT)ashland.edu), Dec 14 2006
%E A124011 Additional comments from Christopher N. Swanson (cswanson(AT)ashland.edu), _R. J. Mathar_, Dec 14 2006