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Search: id:A056106
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| A056106 |
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Second spoke of a hexagonal spiral. |
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+0
9
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| 1, 3, 11, 25, 45, 71, 103, 141, 185, 235, 291, 353, 421, 495, 575, 661, 753, 851, 955, 1065, 1181, 1303, 1431, 1565, 1705, 1851, 2003, 2161, 2325, 2495, 2671, 2853, 3041, 3235, 3435, 3641, 3853, 4071, 4295, 4525, 4761, 5003, 5251, 5505, 5765, 6031, 6303
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = A096777(3*n) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 29 2007
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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-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
E.g.f.: (1+2x+3x^2)exp(x). - Paul Barry (pbarry(AT)wit.ie), Mar 13 2003
a(n)=6*n+a(n-1)-10 (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+1-10=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]
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A054552 for example of square (or octagonal) spiral spoke.
Sequence in context: A141595 A112051 A118436 this_sequence A147382 A164303 A129082
Adjacent sequences: A056103 A056104 A056105 this_sequence A056107 A056108 A056109
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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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