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Search: id:A014209
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| -1, 3, 9, 17, 27, 39, 53, 69, 87, 107, 129, 153, 179, 207, 237, 269, 303, 339, 377, 417, 459, 503, 549, 597, 647, 699, 753, 809, 867, 927, 989, 1053, 1119, 1187, 1257, 1329, 1403, 1479, 1557, 1637, 1719, 1803
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Difference between n-th centered hexagonal number and (2n)^2. - Alonso Delarte (alonso.delarte(AT)gmail.com), Jul 06 2004
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: (Start)
Given the roots to n^2 + 3n - 1, a = -3.302775..., b = .302775...; then
a(n) = (n + 3 + a) * (n + 3 + b). Example: a(3) = 17 = (6 - 3.302...) *
(6 + .302775) (End)
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LINKS
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Anonymous Collective, Centered Hexagonal Numbers.
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FORMULA
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a(n)=2*n+a(n-1) (with a(1)=-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
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EXAMPLE
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For n=2, a(2)=2*2-1=3; n=3, a(3)=2*3+3=9; n=4, a(4)=2*4+9=17 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
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MAPLE
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a:=n->sum(k, k=0..n):seq(a(n)+sum(k, k=3..n), n=1..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 27 2008
with (combinat):seq(fibonacci(3, n)+n-4, n=1..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
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f[n_]:=(n+5)*n-(n+(n+1)); lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
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CROSSREFS
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Cf. A003215.
Cf. A002522.
Sequence in context: A103967 A032400 A004621 this_sequence A057258 A018466 A035107
Adjacent sequences: A014206 A014207 A014208 this_sequence A014210 A014211 A014212
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KEYWORD
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sign,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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