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a(n) = 9n+8.
23

%I #41 Apr 18 2017 07:03:14

%S 8,17,26,35,44,53,62,71,80,89,98,107,116,125,134,143,152,161,170,179,

%T 188,197,206,215,224,233,242,251,260,269,278,287,296,305,314,323,332,

%U 341,350,359,368,377,386,395,404,413,422,431,440,449,458,467,476,485

%N a(n) = 9n+8.

%C Digital root of any number in this sequence = 8. Any partial sum of digits of any number in this sequence also belongs to this sequence. - _Artur Jasinski_, Dec 16 2007

%C a(n-1)^2 - A013656(n) * A010701(n)^2 = 1. - _Vincenzo Librandi_, Nov 19 2010

%C Subsequence of A224829: A224823(a(n)) = 0. - _Reinhard Zumkeller_, Jul 21 2013

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=970">Encyclopedia of Combinatorial Structures 970</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 18*n-a(n-1)+7. - _Vincenzo Librandi_, Nov 19 2010

%F a(0)=8, a(1)=17, a(n) = 2*a(n-1)-a(n-2). G.f.: (8+x)/(1-x)^2. - _Colin Barker_, Jan 24 2012

%p A017257:=n->9*n+8; seq(A017257(n), n=0..100); # _Wesley Ivan Hurt_, Nov 30 2013

%t Array[9*#+8&,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)

%o (Haskell)

%o a017257 = (+ 8) . (* 9)

%o a017257_list = 8 : map (+ 9) a017257_list -- _Reinhard Zumkeller_, Jul 21 2013

%o (PARI) a(n)=9*n+8 \\ _Charles R Greathouse IV_, Sep 28 2015

%Y Cf. A013656, A010701, A008591.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.