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Search: id:A056105
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| A056105 |
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First spoke of a hexagonal spiral. |
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+0
15
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| 1, 2, 9, 22, 41, 66, 97, 134, 177, 226, 281, 342, 409, 482, 561, 646, 737, 834, 937, 1046, 1161, 1282, 1409, 1542, 1681, 1826, 1977, 2134, 2297, 2466, 2641, 2822, 3009, 3202, 3401, 3606, 3817, 4034, 4257, 4486, 4721, 4962, 5209, 5462, 5721, 5986, 6257
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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H. Bottomley, Illustration of initial terms
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
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FORMULA
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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
a(n)=6*n+a(n-1)-11 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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EXAMPLE
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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]
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PROGRAM
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(PARI) a(n)=3*n^2-2*n+1 /* Michael Somos Aug 03 2006 */
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CROSSREFS
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Cf. A054552 for example of square (or octagonal) spiral spoke.
A008810(3n-1)=A056109(-n)=a(n). - Michael Somos Aug 03 2006.
Sequence in context: A131476 A023549 A024850 this_sequence A106058 A086718 A023625
Adjacent sequences: A056102 A056103 A056104 this_sequence A056106 A056107 A056108
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KEYWORD
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easy,nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000
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