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Search: id:A056109
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| A056109 |
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Fifth spoke of a hexagonal spiral. |
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+0
27
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| 1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321, 386, 457, 534, 617, 706, 801, 902, 1009, 1122, 1241, 1366, 1497, 1634, 1777, 1926, 2081, 2242, 2409, 2582, 2761, 2946, 3137, 3334, 3537, 3746, 3961, 4182, 4409, 4642, 4881, 5126, 5377, 5634, 5897, 6166, 6441
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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-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
a(n)=6*n+a(n-1)-7 (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+1-7=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]
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MATHEMATICA
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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]
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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)=A056105(-n)=a(n). - Michael Somos Aug 03 2006.
Sequence in context: A130051 A038795 A066486 this_sequence A023545 A038633 A083045
Adjacent sequences: A056106 A056107 A056108 this_sequence A056110 A056111 A056112
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000
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