Search: id:A056106
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%I A056106
%S A056106 1,3,11,25,45,71,103,141,185,235,291,353,421,495,575,661,753,851,955,
%T A056106 1065,1181,1303,1431,1565,1705,1851,2003,2161,2325,2495,2671,2853,3041,
%U A056106 3235,3435,3641,3853,4071,4295,4525,4761,5003,5251,5505,5765,6031,6303
%N A056106 Second spoke of a hexagonal spiral.
%C A056106 a(n) = A096777(3*n) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 29 2007
%H A056106 H. Bottomley, <a href="a3215.gif">Illustration of initial terms</a>
%H A056106 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 A056106 a(n) = 3n^2-n+1 = a(n-1)+6n-4 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) 
               = A056105(n)+n = A056107(n)-n = A056108(n)-2n = A056109(n)-3n = A003215(n)-4n
%F A056106 E.g.f.: (1+2x+3x^2)exp(x). - Paul Barry (pbarry(AT)wit.ie), Mar 13 2003
%F A056106 a(n)=6*n+a(n-1)-10 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A056106 For n=2, a(2)=6*2+1-10=3; n=3, a(3)=6*3+3-10=11; n=4, a(4)=6*4+11-10=25 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%t A056106 s=1;lst={s};Do[s+=n+1;AppendTo[lst, s], {n, 1, 6!, 6}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A056106 Cf. A054552 for example of square (or octagonal) spiral spoke.
%Y A056106 Sequence in context: A141595 A112051 A118436 this_sequence A147382 A164303 
               A129082
%Y A056106 Adjacent sequences: A056103 A056104 A056105 this_sequence A056107 A056108 
               A056109
%K A056106 easy,nonn,new
%O A056106 0,2
%A A056106 Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000

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