A017653 - OEIS

%I #60 Sep 08 2022 08:44:43

%S 11,23,35,47,59,71,83,95,107,119,131,143,155,167,179,191,203,215,227,

%T 239,251,263,275,287,299,311,323,335,347,359,371,383,395,407,419,431,

%U 443,455,467,479,491,503,515,527,539,551,563,575,587,599,611,623,635

%N a(n) = 12*n + 11.

%C Or, with a different offset, 12*n - 1. In any case, numbers congruent to -1 (mod 12). - _Alonso del Arte_, May 29 2011

%C Numbers congruent to 2 (mod 3) and 3 (mod 4). - _Bruno Berselli_, Jul 06 2017

%H Vincenzo Librandi, <a href="/A017653/b017653.txt">Table of n, a(n) for n = 0..3000</a>

%H John Elias, <a href="/A017653/a017653.png">60*n+55 Triangular Snowflakes</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1000">Encyclopedia of Combinatorial Structures 1000</a>

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

%H Leo Tavares, <a href="/A017653/a017653.jpg">Illustration: Twin Hexagonal 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*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jun 08 2011

%F G.f.: (11+x)/(1-x)^2. - _Colin Barker_, Feb 19 2012

%F A089911(2*a(n)) = 11. - _Reinhard Zumkeller_, Jul 05 2013

%F a(n) = 2*A003215(n+1) - 1 - 2*A003215(n). See Twin Hexagonal Frames illustration. - _Leo Tavares_, Aug 19 2021

%t Array[12*#+11&,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)

%o (PARI) a(n)=12*n+11

%o (Magma) [12*n+11: n in [0..60]]; // _Vincenzo Librandi_, Jun 08 2011

%o (Haskell)

%o a017653 = (+ 11) . (* 12)  -- _Reinhard Zumkeller_, Jul 05 2013

%Y Cf. A003215, A008594, A017533, A017545.

%Y Subsequence of A072065.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_