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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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)
For n>0: a(n) = A176271(n+1,n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 13 2010]
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LINKS
| Wikipedia, Centered Hexagonal Numbers.
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = a(n-1)+2*n+2 (with a(0)=-1). [From Vincenzo Librandi, Nov 20 2010]
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: (-1+6*x-3*x^2)/(1-x)^3. [Colin Barker, Feb 12 2012]
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MAPLE
| 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
| Table[n^2+3*n-1, {n, 0, 100}] (*From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009 *)
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CROSSREFS
| Cf. A003215, A002522.
Sequence in context: A103967 A032400 A004621 * A202253 A057258 A018466
Adjacent sequences: A014206 A014207 A014208 * A014210 A014211 A014212
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KEYWORD
| sign,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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