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0, 6, 24, 54, 96, 150, 216, 294, 384, 486, 600, 726, 864, 1014, 1176, 1350, 1536, 1734, 1944, 2166, 2400, 2646, 2904, 3174, 3456, 3750, 4056, 4374, 4704, 5046, 5400, 5766, 6144, 6534, 6936, 7350, 7776, 8214, 8664, 9126, 9600, 10086, 10584, 11094, 11616
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Number of edges of a complete 4-partite graph of order 4n, K_n,n,n,n. - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Oct 18 2001
Number of edges of the complete bipartite graph of order 7n, K_n,6n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Number of edges in the line graph of the product of two cycle graphs, each of order n, L(C_n x C_n) - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Total surface area of a cube of edge length n. See A000578 for cube volume. See A070169 and A071399 for surface area and volume of a regular tetrahedron and links for the other Platonic solids. - Rick L. Shepherd, Apr 24 2002
a(n) can represented as n concentric hexagons (see example). - Omar E. Pol, Aug 21 2011
Sequence found by reading the line from 0, in the direction 0, 6,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A003154 in the same spiral. - Omar E. Pol, Sep 08 2011
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Wolfram MathWorld, Platonic Solid
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FORMULA
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a(n) = A000290(n)*6. [From Omar E. Pol, Dec 11 2008]
a(n) = A001105(n)*3 = A033428(n)*2. [From Omar E. Pol, Dec 13 2008]
a(n) = 12*n+a(n-1)-6, and a(0)=0. [From Vincenzo Librandi, Aug 05 2010]
G.f.: 6*x*(1+x)/(1-x)^3. [Colin Barker, Feb 14 2012]
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EXAMPLE
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Contribution from Omar E. Pol, Aug 21 2011 (Start):
Illustration of initial terms as concentric hexagons:
.
. 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
.
. 6 24 54
.
(End)
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MAPLE
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seq(6*n^2, n=0..44); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 12}]; lst [From Vladimir Orlovsky, Nov 16 2008]
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CROSSREFS
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Cf. A000217, A000290, A033583, A033428.
Central column of triangle A001283.
Cf. A001105. [From Omar E. Pol, Dec 13 2008]
Cf. A085250, A152734, A152751. Bisection of A032528. - Omar E. Pol, Aug 20 2011
Sequence in context: A083170 A087081 A089973 * A213393 A009943 A028595
Adjacent sequences: A033578 A033579 A033580 * A033582 A033583 A033584
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2001
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STATUS
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approved
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