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%I #45 Apr 03 2024 05:07:32
%S 7,19,31,43,55,67,79,91,103,115,127,139,151,163,175,187,199,211,223,
%T 235,247,259,271,283,295,307,319,331,343,355,367,379,391,403,415,427,
%U 439,451,463,475,487,499,511,523,535,547,559,571,583,595,607,619,631
%N a(n) = 12*n + 7.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H Leo Tavares, <a href="/A017605/a017605.jpg">Illustration: Hexagonal Wheels</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*(12*n+1) - a(n-1) = 2*a(n-1) - a(n-2) with a(0) = 7, a(1) = 19. - _Vincenzo Librandi_, Nov 19 2010
%F a(n) = (n+1)*A016921(n+1) - n*A016921(n). - _Bruno Berselli_, Jan 18 2013
%F a(n) = A003215(n+1) - 6*A000217(n-1). - _Leo Tavares_, Jul 25 2021
%F From _Elmo R. Oliveira_, Apr 02 2024: (Start)
%F G.f.: (7+5*x)/(1-x)^2.
%F E.g.f.: exp(x)*(7 + 12*x).
%F a(n) = A049453(n+1) - A049453(n) = A142241(n)/2. (End)
%t 12*Range[0,200] + 7 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%o (Sage) [i+7 for i in range(525) if gcd(i,12) == 12] # _Zerinvary Lajos_, May 21 2009
%o (PARI) a(n)=12*n+7 \\ _Charles R Greathouse IV_, Jul 10 2016
%Y Cf. A008594, A016921, A017533, A017545, A068229.
%Y Cf. A000217, A003215, A049453, A142241.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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