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A094159
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3 times hexagonal numbers: 3*n*(2*n-1).
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17
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0, 3, 18, 45, 84, 135, 198, 273, 360, 459, 570, 693, 828, 975, 1134, 1305, 1488, 1683, 1890, 2109, 2340, 2583, 2838, 3105, 3384, 3675, 3978, 4293, 4620, 4959, 5310, 5673, 6048, 6435, 6834, 7245, 7668, 8103, 8550, 9009, 9480, 9963, 10458, 10965, 11484
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 3 of A048790.
Sequence found by reading the line from 0, in the direction 0, 3,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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REFERENCES
| Dan Hoey, Bill Gosper and Rich Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
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LINKS
| R. C. Schroeppel, A few mathematical experiments.
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 6*n^2-3*n = 3*n*(2*n-1) = 3*A000384(n) [From Omar E. Pol (info(AT)polprimos.com), Dec 11 2008]
a(n)=12*n+a(n-1)-9 (with a(0)=0) [From Vincenzo Librandi, Nov 16 2010]
G.f.: 3*x*(1+3*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +3; AppendTo[lst, s], {n, 0, 7!, 12}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
| Cf. A000384, A048790.
3 times n-gonal numbers: A045943, A033428, A062741, A152773, A152751, A152759, A152767, A153783, A153448, A153875.
Essentially a bisection of A045943. - Omar E. Pol, Sep 17 2011
Sequence in context: A097989 A039700 A069147 * A138976 A064043 A085789
Adjacent sequences: A094156 A094157 A094158 * A094160 A094161 A094162
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 05 2004
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EXTENSIONS
| More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008
Better definition, corrected offset and edited. - Omar E. Pol (info(AT)polprimos.com), Dec 11 2008
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