%I #52 Jul 30 2024 14:48:34
%S 7,16,25,34,43,52,61,70,79,88,97,106,115,124,133,142,151,160,169,178,
%T 187,196,205,214,223,232,241,250,259,268,277,286,295,304,313,322,331,
%U 340,349,358,367,376,385,394,403,412,421,430,439,448,457,466,475,484
%N a(n) = 9*n + 7.
%C Numbers whose digital root is 7. - _Halfdan Skjerning_, Mar 15 2018
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H J. Laroche & N. J. A. Sloane, <a href="/A004207/a004207.pdf">Correspondence, 1977</a>
%H Leo Tavares, <a href="/A017245/a017245.jpg">Illustration: Triple Triangular Frames</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n)^2 = A156676(n+1) + A017137(n). - _Reinhard Zumkeller_, Jul 13 2010
%F a(n) = 18*n - a(n-1) + 5, with a(0)=7. - _Vincenzo Librandi_, Dec 24 2010
%F G.f.: (7+2*x)/(1-x)^2. - _Vincenzo Librandi_, Apr 30 2015
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - _Vincenzo Librandi_, Apr 30 2015
%t Range[7, 1000, 9] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t Table[9 n + 7, {n, 0, 70}] (* or *) CoefficientList[Series[(7 + 2 x)/(1 - x)^2, {x, 0, 60}], x] (* _Vincenzo Librandi_, Apr 30 2015 *)
%t LinearRecurrence[{2,-1},{7,16},60] (* _Harvey P. Dale_, Jul 30 2024 *)
%o (Magma) [9*n+7: n in [0..60]]; // _Vincenzo Librandi_, Apr 30 2015
%o (PARI) vector(100,n,9*n-2) \\ _Derek Orr_, Apr 30 2015
%Y Cf. A008591, A017233.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_