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A056105
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First spoke of a hexagonal spiral.
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..46.
H. Bottomley, Illustration of initial terms
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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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)-5 (with a(0)=1) [From Vincenzo Librandi, Aug 07 2010]
G.f.: (1-x+6*x^2)/(1-3*x+3*x^2-x^3). [Colin Barker, Jan 04 2012]
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EXAMPLE
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a(1)=6*1+1-5=2; a(2)=6*2+2-5=9; a(3)=6*3+9-5=22 [From Vincenzo Librandi, Aug 07 2010]
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 2, 9}, 50] (* Harvey P. Dale, Nov 02 2011 *)
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PROG
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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: A024850 A237044 A235707 * A212069 A106058 A086718
Adjacent sequences: A056102 A056103 A056104 * A056106 A056107 A056108
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Jun 09 2000
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STATUS
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approved
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