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0, -1, 0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443, 1520, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208, 2303, 2400, 2499, 2600, 2703, 2808, 2915, 3024, 3135, 3248, 3363
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| For n <> +1: numerator of 1-1/(n-1)^2. The associated denominator is A174902(n-1). [Paul Curtz, Dec 05 2010]
a(n) is essentially the case 0 of the polygonal numbers. The polygonal numbers are defined as P_k(n) = Sum_{i=1..n}((k-2)*i-(k-3). Thus P_0(n) = 2*n - n^2 and a(n) = -P_0(n). [Peter Luschny, Jul 08 2011]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = A005563(n-2) = A005563(-n) = A000290(n-1)-1
G.f.: x*(3*x-1)/(1-x)^3; E.g.f.: exp(x)*(x^2-x); - Paul Barry, Mar 27 2007
a(n)=2*n+a(n-1)-3 (with a(0)=0) [From Vincenzo Librandi , Aug 08 2010]
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MATHEMATICA
| Table[ n^2 - 2*n, {n, 0, 60} ]
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PROG
| (PARI a(n)=n^2-2*n;
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CROSSREFS
| Essentially the same as A005563.
Sequence in context: A131386 A132411 A005563 * A066079 A185079 A173569
Adjacent sequences: A067995 A067996 A067997 * A067999 A068000 A068001
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KEYWORD
| easy,sign
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AUTHOR
| George E. Antoniou (george.antoniou(AT)montclair.edu), Feb 06 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 08 2002
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