Search: id:A056105
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%I A056105
%S A056105 1,2,9,22,41,66,97,134,177,226,281,342,409,482,561,646,737,834,937,
%T A056105 1046,1161,1282,1409,1542,1681,1826,1977,2134,2297,2466,2641,2822,3009,
%U A056105 3202,3401,3606,3817,4034,4257,4486,4721,4962,5209,5462,5721,5986,6257
%N A056105 First spoke of a hexagonal spiral.
%H A056105 H. Bottomley, <a href="a3215.gif">Illustration of initial terms</a>
%H A056105 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 A056105 a(n) = 3n^2-2n+1 = a(n-1)+6n-5 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) 
               = A056106(n)-n = A056107(n)-2n = A056108(n)-3n = A056109(n)-4n = 
               A003215(n)-5n
%F A056105 a(n)=6*n+a(n-1)-11 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A056105 For n=2, a(2)=6*2+1-11=2; n=3, a(3)=6*3+2-11=9; n=4, a(4)=6*4+9-11=22 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%o A056105 (PARI) a(n)=3*n^2-2*n+1 /* Michael Somos Aug 03 2006 */
%Y A056105 Cf. A054552 for example of square (or octagonal) spiral spoke.
%Y A056105 A008810(3n-1)=A056109(-n)=a(n). - Michael Somos Aug 03 2006.
%Y A056105 Sequence in context: A131476 A023549 A024850 this_sequence A106058 A086718 
               A023625
%Y A056105 Adjacent sequences: A056102 A056103 A056104 this_sequence A056106 A056107 
               A056108
%K A056105 easy,nonn,new
%O A056105 0,2
%A A056105 Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000

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