%I A056109
%S A056109 1,6,17,34,57,86,121,162,209,262,321,386,457,534,617,706,801,902,1009,
%T A056109 1122,1241,1366,1497,1634,1777,1926,2081,2242,2409,2582,2761,2946,3137,
%U A056109 3334,3537,3746,3961,4182,4409,4642,4881,5126,5377,5634,5897,6166,6441
%N A056109 Fifth spoke of a hexagonal spiral.
%H A056109 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A056109 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A056109 H. Bottomley, <a href="a3215.gif">Illustration of initial terms</a>
%H A056109 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/A2.html">Home page for hexagonal (or triangular) lattice 
               A2</a>
%F A056109 a(n) = 3n^2+2n+1 = a(n-1)+6n-1 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) 
               = A056105(n)+4n = A056106(n)+3n = A056107(n)+2n = A056108(n)+n = 
               A003215(n)-n
%F A056109 a(n)=6*n+a(n-1)-7 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A056109 For n=2, a(2)=6*2+1-7=6; n=3, a(3)=6*3+6-7=17; n=4, a(4)=6*4+17-7=34 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%t A056109 s=1;lst={s};Do[s+=n+5;AppendTo[lst, s], {n, 0, 6!, 6}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 04 2008]
%o A056109 (PARI) a(n)=3*n^2+2*n+1 /* Michael Somos Aug 03 2006 */
%Y A056109 Cf. A054552 for example of square (or octagonal) spiral spoke.
%Y A056109 A008810(3n+1)=A056105(-n)=a(n). - Michael Somos Aug 03 2006.
%Y A056109 Sequence in context: A130051 A038795 A066486 this_sequence A023545 A038633 
               A083045
%Y A056109 Adjacent sequences: A056106 A056107 A056108 this_sequence A056110 A056111 
               A056112
%K A056109 easy,nonn
%O A056109 0,2
%A A056109 Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000