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A017653 a(n) = 12*n + 11.

%I A017653 #63 Apr 12 2025 10:19:50
%S A017653 11,23,35,47,59,71,83,95,107,119,131,143,155,167,179,191,203,215,227,
%T A017653 239,251,263,275,287,299,311,323,335,347,359,371,383,395,407,419,431,
%U A017653 443,455,467,479,491,503,515,527,539,551,563,575,587,599,611,623,635
%N A017653 a(n) = 12*n + 11.
%C A017653 Or, with a different offset, 12*n - 1. In any case, numbers congruent to -1 (mod 12). - _Alonso del Arte_, May 29 2011
%C A017653 Numbers congruent to 2 (mod 3) and 3 (mod 4). - _Bruno Berselli_, Jul 06 2017
%H A017653 Vincenzo Librandi, <a href="/A017653/b017653.txt">Table of n, a(n) for n = 0..3000</a>
%H A017653 John Elias, <a href="/A017653/a017653.png">60*n+55 Triangular Snowflakes</a>.
%H A017653 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1000">Encyclopedia of Combinatorial Structures 1000</a>.
%H A017653 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017653 Leo Tavares, <a href="/A017653/a017653.jpg">Illustration: Twin Hexagonal Frames</a>.
%H A017653 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017653 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jun 08 2011
%F A017653 G.f.: (11+x)/(1-x)^2. - _Colin Barker_, Feb 19 2012
%F A017653 A089911(2*a(n)) = 11. - _Reinhard Zumkeller_, Jul 05 2013
%F A017653 a(n) = 2*A003215(n+1) - 1 - 2*A003215(n). See Twin Hexagonal Frames illustration. - _Leo Tavares_, Aug 19 2021
%F A017653 From _Elmo R. Oliveira_, Apr 12 2025: (Start)
%F A017653 E.g.f.: exp(x)*(11 +  12*x).
%F A017653 a(n) = A016969(2*n+1). (End)
%t A017653 Array[12*#+11&,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)
%o A017653 (PARI) a(n)=12*n+11
%o A017653 (Magma) [12*n+11: n in [0..60]]; // _Vincenzo Librandi_, Jun 08 2011
%o A017653 (Haskell)
%o A017653 a017653 = (+ 11) . (* 12)  -- _Reinhard Zumkeller_, Jul 05 2013
%Y A017653 Cf. A003215, A008594, A016969, A017533, A017545, A089911.
%Y A017653 Subsequence of A072065.
%K A017653 nonn,easy
%O A017653 0,1
%A A017653 _N. J. A. Sloane_