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A085250
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4 times hexagonal numbers: 4*n*(2*n-1).
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20
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0, 4, 24, 60, 112, 180, 264, 364, 480, 612, 760, 924, 1104, 1300, 1512, 1740, 1984, 2244, 2520, 2812, 3120, 3444, 3784, 4140, 4512, 4900, 5304, 5724, 6160, 6612, 7080, 7564, 8064, 8580, 9112, 9660, 10224, 10804, 11400, 12012, 12640, 13284
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) also can represented as n concentric squares (see example). - Omar E. Pol, Aug 21 2011
Sequence found by reading the line from 0, in the direction 0, 4,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 03 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) = A067239(n)/2, for n>0.
Sum(n>0) 1/a(n) = log(2)/2.
a(n) = A000384(n)*4. - Omar E. Pol, Dec 11 2008
a(n) = 16*n+a(n-1)-12 (with a(0)=0). - Vincenzo Librandi, Aug 08 2010
G.f.: 4*x*(1+3*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 04 2012
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EXAMPLE
| Contribution from Omar E. Pol, Aug 21 2011: (Start)
Illustration of initial terms as concentric squares:
.
. o o o o o o o o o o
. o o
. o o o o o o o o o o o o o o
. o o o o o o
. o o o o o o o o o o o o
. o o o o o o o o o o o o
. o o o o o o
. o o o o o o o o o o o o o o
. o o
. o o o o o o o o o o
.
. 4 24 60
.
(End)
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +4; AppendTo[lst, s], {n, 0, 7!, 16}]; lst [From Vladimir Orlovsky, Nov 16 2008]
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CROSSREFS
| Cf. A067239.
Cf. A000384. [From Omar E. Pol, Dec 11 2008]
Cf. A033581, A046092, A152734, A152751, A194274. - Omar E. Pol, Aug 21 2011
Sequence in context: A191778 A157625 A128205 * A166870 A124350 A112611
Adjacent sequences: A085247 A085248 A085249 * A085251 A085252 A085253
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 23 2003
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Nov 13 2005
Added zero, better definition, corrected offset and edited original formula. - Omar E. Pol (info(AT)polprimos.com), Dec 11 2008
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